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hal-00178003, version 1

## Regularity of solutions of the isoperimetric problem that are close to a smooth manifold

Stefano Nardulli () 12

Abstract: In this work we consider a question in the calculus of variations motivated by riemannian geometry, the isoperimetric problem. We show that solutions to the isoperimetric problem, close in the flat norm to a smooth submanifold, are themselves smooth and $C^{2,\alpha }$-close to the given sub manifold. We show also a version with variable metric on the manifold. The techniques used are, among other, the standards outils of linear elliptic analysis and comparison theorems of riemannian geometry, Allard's regularity theorem for minimizing varifolds, the isometric immersion theorem of Nash and a parametric version due to Gromov.

• 1:  Laboratoire de Mathématiques d'Orsay (LM-Orsay)
• CNRS : UMR8628 – Université Paris XI - Paris Sud
• 2:  Dipartimento di Metodi et Modelli Matematici
• Università degli studi di Palermo
• Domain : Mathematics/Differential Geometry
Mathematics/Analysis of PDEs
Mathematics/Metric Geometry
• Keywords : isoperimetric profile – riemannian geometry – geometric measure theory – PDE's methods – regularity theory.
• Comment : 42 pages – 3 figures

• hal-00178003, version 1
• oai:hal.archives-ouvertes.fr:hal-00178003
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• Submitted on: Tuesday, 9 October 2007 19:56:03
• Updated on: Tuesday, 9 October 2007 20:29:14