“Anisotropic Allen-Cahn and convergence to anisotropic area”
Venerdì 5 Dicembre 2025, ore 12:00 - Aula 1BC45 - Alessandro Pigati (Università Bocconi)
Abstract
In this talk we will introduce a PDE way to construct hypersurfaces which are critical for a generalization of area, based on an anisotropic integrand. Namely, we study energy concentration for rescalings of an anisotropic version of Allen-Cahn.
Besides a Gamma-convergence result, we will sketch a proof of the fact that energy of stable critical points (of the rescaled Allen-Cahn) concentrates along an integer rectifiable varifold, a weak notion of hypersurface, using stability (or finite Morse index) to compensate for the lack of monotonicity formulas.
Among the technical ingredients, we will see a generalization of Modica’s bound and a diffuse version of the stability inequality for hypersurfaces.
This is joint work with Antonio De Rosa (Bocconi University).
