Generalized Compactness for Finite Perimeter Sets and Applications to the Isoperimetric Problem

Author(s)

Munoz Flores, Abraham Enrique ^[1] ; Nardulli, Stefano ^[2]

Affiliation

^[1] UERJ Univ Estado Rio De Janeiro, Inst Matemat & Estat, Rio De Janeiro - Brazil

^[2] UFABC Univ Fed ABC, Ctr Matemat Cognicao & Computac, Santo Andre, SP - Brazil

• Document type: Journal article
• Source: JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS; v. 28, n. 1, p. 59-69, JAN 2022.
• Web of Science Citations: 0

Abstract

For a complete noncompact Riemannian manifold with bounded geometry, we prove a ``generalized{''} compactness result for sequences of finite perimeter sets with uniformly bounded volume and perimeter in a larger space obtained by adding limit manifolds at infinity. We extend previous results contained in Nardulli (Asian J Math18(1):1-28,2014), in such a way that the main theorem is a generalization of the generalized existence theorem, i.e., Theorem 1 of Nardulli (Asian J Math18(1):1-28,2014). We replaceC(2,alpha)locally asymptotic bounded geometry withC(0)locally asymptotic bounded geometry. (AU)

• FAPESP's process: 18/22938-4 - Boundary regularity for area minimizing currents
• Grantee: Stefano Nardulli
• Support Opportunities: Scholarships abroad - Research