Sets of finite perimeter and geometric measure theory

Published/accepted papers

  1. Regularity of codimension-1 minimizing currents under minimal assumptions on the integrand
    J. Diff. Geom. 106 (2017), no. 3, 371-391.
  2. BMO-type norms related to the perimeter of sets (with L. Ambrosio, J. Bourgain, and H. Brezis)
    Comm. Pure Appl. Math. 69 (2016), no.6, 1062-1086.
  3. How to recognize convexity of a set from its marginals (with D. Jerison)
    J. Funct. Anal. 266 (2014), no. 3, 1685-1701.
  4. On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to half-spaces (with L. Ambrosio and E. Runa)
    Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 24 (2013), no. 1, 111-122.
  5. Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces (with L. Ambrosio)
    Ann. Fac. Sci. Toulouse Math. (6) 20 (2011), no. 2, 407-438.
  6. A simple proof of the Morse-Sard theorem in Sobolev spaces
    Proc. Amer. Math. Soc. 136 (2008), no. 10, 3675-3681.

Lecture notes and reviews

  1. Regularity theory for local and nonlocal minimal surfaces: an overview (with M. Cozzi)
    Nonlocal and nonlinear diffusions and interactions: new methods and directions, 117-158,
    Lecture Notes in Math., 2186, Fond. CIME/CIME Found. Subser., Springer, Cham, 2017.
  2. Perimeter of sets and BMO-type norms (with L. Ambrosio, J. Bourgain and H. Brezis)
    C. R. Math. Acad. Sci. Paris 352 (2014), no. 9, 697-698.