Geometric Analysis and Topology Seminar

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Min-max construction of anisotropic CMC surfaces

Speaker: Antonio De Rosa, University of Maryland

Location: Warren Weaver Hall 512

Videoconference link: https://nyu.zoom.us/j/95759976381

Date: Friday, March 24, 2023, 11 a.m.

Synopsis:

Abstract: We prove the existence of nontrivial closed surfaces with constant anisotropic mean curvature with respect to elliptic integrands in closed smooth 3-dimensional Riemannian manifolds. The constructed min-max surfaces are smooth with at most one singular point. The constant anisotropic mean curvature can be fixed to be any real number. In particular, we partially solve a conjecture of Allard [Invent. Math.,1983] in dimension 3.