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Talk

Minimal sets in Riemannian manifolds

  • Vincent Feuvrier (Institut de Mathématiques de Toulouse)
A3 01 (Sophus-Lie room)

Abstract

We study the existence of sets that minimize their measure amongst a family stable under homotopy in a compact, boundaryless Riemannian manifold. We consider the problem in the category of sets without resorting to the weakened notions of Federer (currents) or Almgren (varifolds). This setting allows to free oneself of additional regularity assumptions such as orientability, or even rectifiability of the competitors. In this talk, I will try to explain how a polyhedral approximation process inspired by Federer can be generalized to this setup and make up for the lack of compactness of the set-based approach.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of This Seminar

  • Mar 11, 2024 tba with Carlos Román Parra
  • Mar 15, 2024 tba with Esther Bou Dagher