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math.AP2021
(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…
math.AP2021
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…
math.AP2021
Area minimizing hypersurfaces modulo : a geometric free-boundary problem
Camillo De Lellis, Jonas Hirsch, Andrea Marchese +2
We consider area minimizing -dimensional currents in complete Riemannian manifolds of dimension . For odd moduli we prove that, away from a clos…