Prof. Dr. Alessio Figalli

Submitted papers and preprints

  1. Stable solutions of the Allen–Cahn equation in dimension three are one-dimensional (with H. Chan, X. Fernández-Real, E. Florit-Simon, and J. Serra)
  2. The generic structure of the singular set in the Stefan problem (with G. Colombo)
  3. A dimension-free interpolation of Caffarelli’s contraction theorem (with B. Ammari)
  4. Stable semilinear elliptic equations: $\varepsilon$-regularity à la Brezis and dimensional bounds for the singular set (with F. Franceschini)
  5. Sharp Stability of Alexandrov's Theorem for $C^1$ Domains in the Small-Excess Regime (with Y. Ru-Ya Zhang)
  6. Global regularity and free boundary geometry in the planar Rochet-Choné model (with S. Chen and Y. Ru-Ya Zhang)
  7. Sharp Quantitative Stability for the Prékopa-Leindler and Borell-Brascamp-Lieb Inequalities (with P. van Hintum and M. Tiba)
  8. Constraint maps: singularities vs free boundaries (with A. Guerra, S. Kim, and H. Shahgholian)
  9. Sharp stability of the Brunn-Minkowski inequality via optimal mass transportation (with P. van Hintum and M. Tiba)
  10. Sharp quantitative stability of the Brunn-Minkowski inequality (with P. van Hintum and M. Tiba)
  11. Regularity theory for nonlocal obstacle problems with critical and subcritical scaling (with X. Ros-Oton and J. Serra)
  12. Effective dimension of machine learning models (with A. Abbas, D. Sutter, and S. Woerner)