35 citations · 45 across the 10 of their papers we have counts for
16 papers
Rectifiability of the singular set and uniqueness of tangent cones for semicalibrated currents
Paul Minter, Davide Parise, Anna Skorobogatova +1
We prove that the singular set of an -dimensional integral current in , semicalibrated by a -form is countably -rectifiable.…
A strong maximum principle for minimizers of the one-phase Bernoulli problem
Nick Edelen, Luca Spolaor, Bozhidar Velichkov
We prove a strong maximum principle for minimizers of the one-phase Alt-Caffarelli functional. We use this to construct a Hardt-Simon-type foliation associated to any 1-homogenous…
Fine structure of the singular set of area minimizing hypersurfaces modulo
Camillo De Lellis, Jonas Hirsch, Andrea Marchese +2
Consider an area minimizing current modulo of dimension in a smooth Riemannian manifold of dimension . We prove that its interior singular set is, up to a relatively c…
(Quasi-)conformal methods in two-dimensional free boundary problems
Guido De Philippis, Luca Spolaor, Bozhidar Velichkov
In this paper we study the local behavior of solutions to some free boundary problems. We relate the theory of quasi-conformal maps to the regularity of the solutions to nonlinear…
Rectifiability and almost everywhere uniqueness of the blow-up for the vectorial Bernoulli free boundaries
Guido De Philippis, Max Engelstein, Luca Spolaor +1
We prove that for minimizers of the vectorial Alt-Caffarelli functional the two-phase singular set of the free boundary is rectifiable and the blow-up is unique almost everywhere o…
On the logarithmic epiperimetric inequality for the obstacle problem
Luca Spolaor, Bozhidar Velichkov
We give three different proofs of the log-epiperimetric inequality at singular points for the obstacle problem. In the first, direct proof, we write the competitor explicitly; the…