Analysis Seminar

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Min-max construction of anisotropic minimal hypersurfaces

Speaker: Antonio De Rosa, Bocconi University

Location: Warren Weaver Hall 1302

Date: Thursday, November 14, 2024, 11 a.m.

Synopsis:

We use the min-max construction to find closed optimally regular hypersurfaces with constant anisotropic mean curvature with respect to elliptic integrands in closed n-dimensional Riemannian manifolds. The critical step is to obtain a uniform upper bound for density ratios in the anisotropic min-max construction. This confirms a conjecture posed by Allard [Invent. Math., 1983]. The talk is based on joint work with G. De Philippis and Y. Li.