Asian Journal of Mathematics

Volume 18 (2014)

Number 1

Generalized existence of isoperimetric regions in non-compact Riemannian manifolds and applications to the isoperimetric profile

Pages: 1 – 28

DOI: http://dx.doi.org/10.4310/AJM.2014.v18.n1.a1

Author

Stefano Nardulli (Departamento de Matemática do Instituto de Matem´atica, Universidade Federal do Rio de Janeiro, Brasil)

Abstract

For a complete noncompact Riemannian manifold with smoothly bounded geometry, we prove the existence of isoperimetric regions in a larger space obtained by adding finitely many limit manifolds at infinity. As one of many possible applications, we extend properties of the isoperimetric profile from compact manifolds to such noncompact manifolds.

Keywords

existence of isoperimetric region, isoperimetric profile

2010 Mathematics Subject Classification

49Q05, 49Q20, 53A10, 58E99

Full Text (PDF format)