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Geometric Analysis Seminar

Uniqueness of critical points of the anisotropic isoperimetric problem.

Antonio De Rosa, University of Maryland

Location:  via Zoom, https://rutgers.zoom.us/j/93880280324
Date & time: Tuesday, 06 October 2020 at 2:50PM - 3:50PM

Abstract
The anisotropic isoperimetric problem consists in enclosing a prescribed volume in a closed hypersurface with least anisotropic energy. Although its solutions, referred to as Wulff shapes, are well understood, the characterization of the associated critical points is more subtle. In this talk we present a uniqueness result: Given an elliptic integrand of class \(C^{2,\alpha}\), we prove that finite unions of disjoint (but possibly mutually tangent) open Wulff shapes with equal radii are the only volume-constrained critical points of the anisotropic surface energy among all finite perimeter sets with reduced boundary almost equal to its closure. To conclude, we will discuss a quantitative stability for this rigidity theorem.
Joint work with Mario Santilli and Slawomir Kolasinski.

Please email Daniel Ketover at
dk927@rutgers.edu
to either be added to the list of invitees or to attend a particular talk.

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