University of Tennessee - Geometric analysis seminar

Spring 2019

Thursday, January 17, 17:10, A113

Robin Neumayer (Northwestern University)

Title: On minimizers and critical points for anisotropic isoperimetric problems.

Abstract: Anisotropic surface energies are a natural generalization of the perimeter functional that arise, for instance, in scaling limits for certain probabilistic models on lattices. This talk focuses on two recent results concerning isoperimetric problems with anisotropic surface energies. In the first part of the talk, we will discuss a weak characterization of critical points in the anisotropic isoperimetric problem (joint work with Delgadino, Maggi, and Mihaila). The second portion of the talk focuses on energy minimizers in an anisotropic variant of a model for atomic nuclei (joint work with Choksi and Topaloglu).

Thursday, January 31, 17:10, A113

Christos Mantoulidis (Massachusetts Institute of Technology)

Title: Positive scalar curvature with skeleton singularities.

Abstract: This is joint work with Chao Li. We study positive scalar curvature on the regular part of Riemannian manifolds with singular, uniformly Euclidean metrics that consolidate Gromov's scalar curvature polyhedral comparison theory and edge metrics that appear in the study of Einstein manifolds. We show that, in all dimensions, edge singularities with cone angles ≤ 2 π along codimension-2 submanifolds do not affect the Yamabe type. In three dimensions, we prove the same for more general singular sets, which are allowed to stratify along 1-skeletons, exhibiting edge singularities (angles ≤ 2 π) and arbitrary L isolated point singularities.

Thursday, February 28, 17:10, A113

Nicholas Edelen (Massachusetts Institute of Technology)

Title: A global bound for the singular set of area-minimizing hypersurfaces.

Abstract: We give an a priori bound on the (n−7)-dimensional measure of the singular set for an area-minimizing n-dimensional hypersurface, in terms of the geometry of its boundary.

Thursday, March 7, 18:10, A113

André Neves (University of Chicago)

Title: Density and equidistribution of minimal hypersurfaces.

Abstract: We will show that on closed manifolds, the set of all closed minimal hypersurfaces is dense for generic metrics. Moreover, under the same conditions, we will also show the existence of a sequence of minimal hypersurfaces that become equidistributed. These are the first results of this kind for minimal hypersurfaces. This is joint work with Irie, Marques and Song.

André will also give a colloquium talk on Friday at 14:35.

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