Prof. Dr. Tristan Rivière

List of all publications

  1. Area Variations Under Legendrian Constraint. Peking Mathematical Journal DOI : 10.1007/s42543-024-00090-y
  2. with F. Gaia and G. Orriols A variational construction of Hamiltonian stationary surfaces with isolated Schoen–Wolfson conical singularities. Comm. Pure Appl. Math. to appear 2024.
  3. Area Variations under pointwise Lagrangian and Legendrian Constraints. Abel Symposium 2024 to appear. [PDF ]
  4. with F. Palmurella The Parametric Willmore Flow J. für die reine & angewandte Math. . 811 (2024), 1–91.
  5. Almost monotonicity formula for H-minimal Legendrian surfaces in the Heisenberg group. Comm. Pure Appl. Math. 77(2024), no.3, 1940–1957
  6. with F. Gaia A Variational Approach to S^1 harmonic maps and applications. J. Functional Analysis 285 (2023), no 11
  7. with R. Caniato: The Unique Tangent Cone Property for Weakly Holomorphic Maps into Projective Algebraic Varieties. Duke Math. J. 172 (2023), no. 13, 2471-2536.
  8. With A. Michelat : Pointwise Expansion of Degenerating Immersions of Finite Total Curvature. Journal of Geometric Analysis 33 (2023), no. 1, 91 pp. [PDF ]
  9. With F. Palmurella : The parametric approach to the Willmore flow Advances in Mathematics 400 (2022) 48 pp. [PDF ]
  10. With F. Da Lio and J. Wettstein : Integrability by compensation for Dirac Equation. Transaction of the AMS 375 (2022), no 6, 4477-4511 [PDF ]
  11. With F. Da Lio and J. Wettstein : Bergman-Bourgain-Brezis-type Inequality. J. of Functional Analysis 281 (2021), no. 9, Paper No. 109201. [PDF ]
  12. With A. Paunoiu : Sobolev Connections and Holomorphic Structures over Kähler Surfaces. J. of Functional Analysis 280 (2021), no. 12, Paper No. 109003, 77 pp. [PDF ]
  13. Harmonic Maps from S^3 into S^2 with low Morse Index. J. of Differential Geom. 125 (2023), no 1, 173-185[PDF ]
  14. With A. Michelat : The Classification of Branched Willmore Spheres in the 3-Sphere and the 4-Sphere. Annales Scientifiques de l'Ecole Normale Supérieure 55 (2022), no 5, 1199-1288 [PDF ] Computer assisted part of the proof [PDF ]
  15. With F. Da Lio : Critical Chirality in Elliptic Systems. Annales Inst. Henri Poincaré - Analyse non linéaire 38 (2021), no. 5, 1373–1405. [PDF ]
  16. Exploring the unknown: the work of Louis Nirenberg in Partial Differential Equations. EMS Surveys in Mathematical Sciences 9 (2022),no 1, 1-29 [PDF ]
  17. with F. Da Lio Three-commutators revisited. Comm. Partial Differential Equations 45 (2020), no. 8, 931–969. [PDF ]
  18. with F. Da Lio and F. Palmurella: A resolution of the Poisson problem for elastic plates. Arch. Ration. Mech. Anal. 236 (2020), no. 3, 1593–1676. [PDF ]
  19. Infinitely many minimal hypersufaces in low dimensions Astérisque No. 422, Séminaire Bourbaki. Vol. 2018/2019. Exposés 1151–1165 (2020), Exp. No. 1165 [PDF ] Video : https://www.youtube.com/watch?v=afhjxjHEUl4
  20. with A. Pigati: A Proof of the Multiplicity One Conjecture for Min-Max Minimal Surfaces in Arbitrary Codimension. Duke Math. J. 169 (2020), no. 11, 2005–2044. [PDF ]
  21. with A. Pigati: The regularity of parametrized integer stationary varifolds in two dimensions. Comm. Pure Appl. Math. 73 (2020), no. 9, 1981–2042. [PDF, 608 KB]
  22. Lower Semi-Continuity of the Index in the Viscosity Method for Minimal Surfaces. Int. Math. Res. Notices 2021, no. 8, 5651-5675. [PDF, 386 KB]
  23. Willmore Minmax Surfaces and the Cost of the Sphere Eversion. J. Eur. Math. Soc. (JEMS) 23 (2021), no. 2, 349-423 [PDF, 612 KB]
  24. The Variations of Yang-Mills Lagrangian Progress in Mathematics, Springer Vol. 333, (2020) 305-379 (2020) [PDF ]
  25. with P. Laurain: Optimal estimate for the gradient of Green's function on degenerating surfaces and applications. Comm. Anal. Geom. 26 (2018), no. 4, 887-913. [PDF, 411 KB]
  26. with Y. Bernard: Uniform regularity results for critical and subcritical surface energies Calc. Var. Partial Differential Equations 58 (2019), no. 1, Art. 10, 39 pp. [PDF, 527 KB]
  27. The regularity of conformal target harmonic maps Calc. Var. Partial Differential Equations 56 (2017), no. 4. [PDF, 333 KB]
  28. with P. Laurain: Energy Quantization of Willmore surfaces at the boundary of the Moduli Space. Duke Math. J. 167 (2018), no. 11, 2073–2124. [PDF, 1016 KB]
  29. A Viscosity Method in the Min-Max Theory of Minimal Surfaces Publ. Math. Inst. Hautes Études Sci. 126 (2017), 177-246. [PDF, 544 KB]
  30. with Y. Bernard: Ends of immersed minimal and Willmore surfaces in asymtotically flat spaces Comm. Anal. Geom. 28 (2020), no. 1, 1–57. [PDF, 920 KB]
  31. Tori in $S^3$ minimizing locally the conformal volume J. Geometric Analysis 26 (2016), no. 3, 2322-2382. [PDF, 416 KB]
  32. with A. Michelat: A Viscosity Method for the Min-Max Construction of Closed Geodesics ESAIM Control Optim. Calc. Var. 22 (2016), no. 4, 1282-1324. [PDF, 544 KB]
  33. Méthodes de min-max et la conjecture de Willmore Séminaire Bourbaki, Astérisque No. 367-368 (2015), Exp. No. 1080, viii, 179-217. [PDF, 368 KB]
  34. Critical weak immersed Surfaces within Sub-manifolds of the Teichmüller Space. Advances in Math. 283 (2015), 232-274. [PDF, 320 KB]
  35. with F. Da Lio and L. Martinazzi: Blow-up analysis of a non-local Liouville-type Equation, Analysis and P.D.E. 8 (2015), no. 7, 1757-1805. [PDF, 976 KB]
  36. with P. Laurain: Optimal estimate for the gradient of Green functions on degenerating surfaces and applications Comm. Anal. Geom. 26 (2018), no. 4, 887–913. [PDF, 232 KB]
  37. with M. Petrache: The resolution of the Yang-Mills Plateau Problem in Super-critical Dimensions Advances in Math. 316 (2017), 469-540. [PDF, 560 KB]
  38. Abel Prize Lecture The work of Louis Nirenberg in Partial Differential Equations. Notices Amer. Math. Soc. 63 (2016), no. 2, 120-125. [PDF, 352 KB] Video : https://www.youtube.com/watch?v=VJWjUielWY0
  39. with A. Mondino: A frame energy for immersed tori and applications to regular homotopy classes J. Differential Geom. 104 (2016), no. 1, 143-186. [PDF, 336 KB]
  40. with R. Hardt: Sequential Weak Approximation for Maps of Finite Hessian Energy Calc. Var. Partial Differential Equations 54 (2015), no. 3, 2713-2749. [PDF, 352 KB]
  41. with M. Petrache: Global Gauges and Extensions in Optimal Spaces Analysis & P.D.E. 7 (2014), no. 8, 1851-1899. [PDF, 568 KB]
  42. with A. Mondino: Immersed Spheres of Finite Total Curvature into Manifolds. Adv. Calc. Var. 7 (2014), no. 4, 493-538. [PDF, 336 KB]
  43. with L. Keller and A. Mondino: Embedded surfaces of arbitrary genus minimizing the Willmore energy under isoperimetric constraint Arch. Ration. Mech. Anal. 212 (2014), no. 2, 645-682. [PDF, 336 KB]
  44. with P. Laurain: Angular Energy Quantization for Linear Elliptic Systems with Antisymmetric Potentials and Applications. Analysis & P.D.E. 7 (2014), no. 1, 1-41. [PDF, 448 KB]
  45. with Y. Bernard: Energy Quantization for Willmore Surfaces and Applications. Annals of Math. (2) 180 (2014), no. 1, 87-136. [PDF, 384 KB]
  46. Variational Principles for immersed Surfaces with L2-bounded Second Fundamental Form. , J. Reine Angew. Math. 695 (2014), 41-98. [PDF, 792 KB]
  47. with A. Mondino: Willmore Spheres in Compact Riemannian Manifolds. Adv. Math. 232 (2013), 608-6076. [PDF, 584 KB]
  48. Sequences of Smooth Global Isothermic Immersions. Comm. P.D.E. 38 (2013), no. 2, 276-303. [PDF, 264 KB]
  49. with P. Laurain: Energy Quantization for Biharmonic Maps. Adv. Calc. Var. 6 (2013), no. 2, 191-216. [PDF, 200 KB]
  50. with Y. Bernard: Singularity removability at branch points for Willmore surfaces. Pacific J. Math. 265 (2013), no. 2, 257-311. [PDF, 448 KB]
  51. Lipschitz conformal Immersions from degenerating Riemann Surfaces with L2-bounded Second Fundamental Forms. Adv. Calc. Var. 6 (2013), no. 1, 1-31. [PDF, 248 KB]
  52. with C. Bellettini: The regularity of Special Legendrian Integral Cycles. Ann. Sc. Norm. Sup. Pisa (5) 11 (2012), no. 1, 61-142. [PDF, 752 KB]
  53. The role of conservation laws in the analysis of conformally invariant problems. Topics in modern regularity theory, 117-167, CRM Series, 13, Ed. Norm., Pisa, 2012.
  54. with M. Petrache: Weak closure of singular abelian L^p-bundles in 3-dimensions. Geometric And Functional Analysis 21 (2011), no. 6, 1419-1442. [PDF, 616 KB]
  55. Sub-criticality of Schrödinger Systems with Antisymmetric Potentials. J. Math. Pures Appl. (9) 95 (2011), no. 3, 260-276. [PDF, 216 KB]
  56. with F. Da Lio: Sub-criticality of non-local Schrödinger systems with antisymmetric potentials and applications to half harmonic maps. Advances in Math. 227 (2011), no. 3, 1300-1348. [PDF, 744 KB]
  57. with Y. Bernard: An Energy Gap Phenomenon for Willmore Spheres, preprint 2011. [PDF, 128 KB]
  58. with F. Da Lio: 3-term commutator estimates and the regularity of 1/2-harmonic maps into spheres, Analysis and PDE 4 (2011), no. 1, 149--190. [PDF, 336 KB]
  59. with Y. Bernard: Local Palais Smale Sequences for the Willmore Functional. Comm. Analysis and Geom. 19 (2011), no. 3, 563-599. [PDF, 272 KB]
  60. with D. Pumberger: Uniqueness of tangent cones for semi-calibrated 2-cycles. Duke J. Math., 152 (2010), no 3, 441-480. [PS, 1160 KB]
  61. with M. Blaser: A Minimality property for entropic solutions to scalar conservation laws in 1 + 1 dimensions, Comm. P.D.E. 35 (2010), no. 10, 1763-1801. [PDF, 288 KB]
  62. with Gang Tian: The Singular Set of 1-1 Integral Currents, Annals of Math. (2) 169 (2009), no. 3, 741-794. [PDF, 440 KB]
  63. Analysis aspects of Willmore surfaces. Inventiones Math., 174 (2008), no.1, 1-45. [PDF, 336 KB]
  64. The role of Integrability by Compensation in Conformal Geometric Analysis. Analytic aspects of problems from Riemannian Geometry,SMF, Séminaires et Congrès, 19, (2008). [PDF, 312 KB]
  65. with T. Kessel: Singular bundles with bounded L^2 curvatures. Boll. U.M.I. volume dedicated to the memory of Guido Stampacchia, 1 (2008), no. 3, 881-901. [PDF, 208 KB]
  66. with R. Hardt: Connecting Rational Homotopy Type Singularities. Acta Math., 200 (2008), no. 1, 15-83. [PS, 1528 KB]
  67. with T. Lamm: Conservation laws for fourth order systems in four dimensions. Comm. P.D.E., 33 (2008), no. 1-3, 245-262. [PS, 632 KB]
  68. Error Analysis for the Willmore-Helfrich Functional, Oberwolfach Reports, Mathematics of Biological Membranes (2008), 2305-2309 (2008). [PDF, 88 KB]
  69. with M. Struwe: Partial regularity for harmonic maps and related problems. Comm. Pure and App. Math., 61 (2008), no. 4, 451-463. [PS, 344 KB]
  70. Conservation laws for conformally invariant variational problems. Inventiones Math., 168 (2007), no. 1, 1-22. [PS, 384 KB]
  71. Sobolev critical exponents of rational homotopy groups. Quarterly J. of Pure and App. Math., issue in honor of L.Simon, 3 (2007), no. 2, 615-630. [PS, 360 KB]
  72. Conservation laws for solutions to Schrödinger systems with antisymmetric potentials. GDR CNRS EDP Evian (2006). [PS, 328 KB]
  73. with P. Strzelecki: A sharp non-linear Gagliardo-Nirenberg-type estimate and applications to the regularity of elliptic systems. Comm. P.D.E., 30 (2005), no. 4-6, 589-604. [PS, 192 KB]
  74. Approximating J-holomorphic curves by holomorphic ones. Calc. Var. P.D.E., 21 (2004), no. 3, 273-285. [PS, 208 KB]
  75. A lower-epiperimetric inequality for area minimizing surfaces. Comm. Pure and App. Math., 57 (2004), no. 3, 273-285. [PS, 208 KB]
  76. with G. Tian: The singular set of J-holomorphic maps into algebraic varieties. Journal für Reine und Angew. Math., 570 (2004), 47-87. [PS, 528 KB]
  77. Some problems from the non-linear analysis of high dimensional Gauge Theory.Variational Analysis and applications, Volume in memory of G. Stampacchia, Erice-Sicily, (2003).
  78. with C. De Lellis: The Rectifiability of Entropy Measures in one Space dimension. Journal de Math. Pures et App., 82, (2003), no. 10, 1343-1367. [PS, 1288 KB]
  79. Bubbling, quantization and regularity issues in geometric non-linear analysis, ICM Beijing (2002). [PS, 192 KB]
  80. with L. Ambrosio, B. Kirchheim and M. Lecumberry: Rectifiability of defect measures arising in micromagnetic domains, Volume dedicated to the 80th birthday of O. Ladyzhenskaya, 29-60, Int. Math. Ser. (N.Y.), Kluwer/Plenum. [PS, 416 KB]
  81. with L. Ambrosio and M. Lecumberry: A viscosity property of minimizing micromagnetic configurations. Comm. Pure and App. Math., 56 (2003), no. 6, 681-688. [PS, 160 KB]
  82. with Y. Meyer: Partial Regularity result for a class of stationary Yang-Mills Fields. Rev. Math. Iberoamericana, 19, (2003), no.1, 195-219. [PS, 408 KB]
  83. with S. Serfaty: Compactness, kinetic formulation and entropies for a problem related to Micromagnetics. Comm. Partial Differential Equations, 28 (2003), no. 1-2, 249-269. [PS, 160 KB]
  84. with M.R. Pakzad: Weak density of smooth maps for the Dirichlet Energy between manifolds. Geom. Funct. Anal., 13 (2003), no. 1, 223-257. [PS, 336 KB]
  85. with R. Hardt: Connecting Topological Hopf Singularities. Ann. Sc. Norm. Sup. Pisa Cl. Sci. (5) 2 (2003), no. 2, 287-344. [PS, 528 KB]
  86. High-dimensional Helicities and rigidity of linked Foliations. Asian J. Math., 6, (2002), no. 3, 505-533. [PS, 536 KB]
  87. with M. Lecumberry: Regularity property for Micromagnetic configurations having zero jump energy. Calc Var. and P.D.E., 15 (2002), no. 3, 389-402. [PS, 232 KB]
  88. with F. Alouges and S. Serfaty: Wall energies of micromagnetic materials with strong planar anisotropy, ESAIM Controle Opt. Calculus Variations, a tribute to J.L. Lions (2002). [PS, 6128 KB]
  89. Parois et vortex en micromagnétisme. Journées équations aux dérivées partielles, (Forges-les-eaux, 2002), Exp. No. XIV, Univ. Nantes, Nantes 2002. [PS, 224 KB]
  90. with M. Lecumberry: The rectifiability of shock waves for the solutions of genuinely non-linear scalar conservation laws in 1+1 D, PhD Thesis of M. Lecumberry, Nantes (2002). [PS, 224 KB]
  91. Towards Jaffe and Taubes Conjectures in the strongly repulsive limit. Manuscripta Mathematica, 108 (2002), no. 2, 217-273. [PS, 568 KB]
  92. Interpolation Spaces and Energy Quantization for Yang-Mills Fields. Comm. Anal. Geom., 10 (2002), no. 4, 683-708. [PS, 216 KB]
  93. with F.H. Lin: Energy Quantization for Harmonic Maps. Duke J. Math. (2002), no. 1, 177-193. [PS, 184 KB]
  94. with F.H. Lin: Quantization property for moving Line vortices. Comm. Pure App. Math., 54, (2001), no. 7, 826-850. [PS, 376 KB]
  95. with A. Aftalion: Vortex energy and vortex bending for a rotating Bose-Einstein condensate, Physical Review A, 64, 043611 (2001), 1-7. [PS, 408 KB]
  96. with S. Serfaty: Limiting domain wall Energy for a Problem related to Micromagnetics. Comm. Pure App. Math., 54, (2001), no. 3, 294-338. [PS, 464 KB]
  97. with F.H. Lin: A Quantization property for static Ginzburg-Landau Vortices. Comm. Pure App. Math., 54, (2001), no. 2, 206-228. [PS, 352 KB]
  98. On Dense subsets of $H^{\frac{1}{2}}(S^2,S^1)$}. Glob. Anal. and Geom., 18 (2000), no. 5, 517-528.
  99. with R. Hardt: Ensembles singuliers topologiques dans les espaces fonctionnels entre variétés. Séminaire EDP, École Polytechnique, No.7, 14p, (2000-2001). [PS, 208 KB]
  100. Ginzburg Landau Vortices - The static Model. Bourbaki Seminar exposé no 868, (1999/2000), Altérisque, no. 276 (2000), 73-103.
  101. with F.H. Lin: Complex Ginzburg-Landau Equations in high dimensions and codimension 2 Minimal surfaces, J. European Math. Soc., 1, (1999) 3, 237-311.
  102. On the use of differential forms for the Skyrme Problem, Letters in Math. Phy., 45, 3, 229-238 (1998).
  103. Asymptotic analysis for the Ginzburg-Landau Equations. Mini-course ETH Zürich 1997, Bolletino UMI, 2-B, (1999) 8, no. 3, 537-575. [PDF, 288 KB]
  104. Minimizing Fibrations and $p$-Harmonic maps in Homotopy Classes from $S^3$ into $S^2$. Comm. Anal. Geom., 6, (1998), no. 3, 427-483
  105. with F. Pacard: On the set of Minimizers of the Ginzburg-Landau Functional in dimension 2. Harmonic Morphisms, Harmonic Maps and related Topics, (Brest 1997), 243-246, Pitman Research notes in Math. Series, CRC Press, 413.
  106. with D. Ye: Resolutions of the prescribed volume form equation. Non linear Diff. Equations and Applications, 3, (1996), no. 3, 323-369. [PS, 576 KB]
  107. Line vortices in the $U(1)$-Higgs Model. ESAIM Controle Optimal Calc. Var., vol 1, 1995/96, 77-167. [PDF, 644 KB]
  108. Lignes de tourbillon dans le modèle abélien de Higgs. C.R.Acad.Sc. Paris, 321, (1995), no. 1, 73-76.
  109. with F. Bethuel: Vortices for a variational problem related to Superconductivity. Annales de l'I.H.P., Analyse non linéaire, 12 (1995), no. 3, 243-303.
  110. Everywhere discontinuous Harmonic Maps into Spheres. Acta Matematica, 175, (1995), no. 2, 197-226.
  111. with F. Bethuel: Fonctionnelle de Ginzburg-Landau pour la supraconductivité, Exposé au Séminaires EDP, École Polytechnique, Exp. No. 16, 12p. (mars 1994).
  112. with D. Ye: Une résolution de l'équation à forme volume prescrite. C.R.Acad.Sc. Paris, I Math., 319, (1994), no. 1, 25-28.
  113. with H. Brezis and F. Merle: Quantization effects for $-\Delta u=u, (1-|u|^2)$ in ${\mathbb{R}}^2$}. Arch. Rat. Mech. and Anal, 126, (1994),pp 123-145.
  114. with H. Brezis and F. Merle: Effets de quantification pour $-\Delta u=u, (1-|u|^2)$ sur ${\mathbb{R}}^2$}. C.R.Acad.Sc. Paris, I Math., 317, (1993), no. 1, pp 57-60.
  115. Harmonic maps with values into Torii of revolution, published in "Applications harmoniques entre variétés": Thèse de l'université Paris 6, (1993).[PDF]
  116. Flot des applications harmoniques en dimension deux, published in "Applications harmoniques entre variétés": Thèse de l'université Paris 6, (1993).[PDF]
  117. Infinités des applications harmoniques à valeur dans une sphère pour une condition au bord donnée, published in "Applications harmoniques entre variétés": Thèse de l'université Paris 6, (1993).[PDF]
  118. Harmonic maps from $B^3$ into $S^2$ having a line of singularities, published in "Applications harmoniques entre varietes": Thèse de l'université Paris 6, (1993).[PDF]
  119. Applications harmoniques partout discontinues, Séminaires EDP, École Polytechnique, XIX, (1992).
  120. Applications harmoniques de $B^3$ dans $S^2$ partout discontinues. C.R.Acad.Sc. Paris, I Math., 314, (1992), no. 10, 719-723.
  121. Applications harmoniques de $B^3$ dans $S^2$ ayant une ligne de singularités. C.R.Acad.Sc. Paris, I Math., 313, (1991), no. 9, 583-587.
  122. with Itai Shafrir: Asymptotic analysis of minimizing harmonic maps of region bounded by two cylinders, C.R.Acad.Sc. Paris, 313, (1991), pp 503-508.