The area blow up set for bounded mean curvature submanifolds with respect to elliptic surface energy functionals

Guido De Philippis, Antonio De Rosa, Jonas Hirsch

Research output: Contribution to journalArticle

Abstract

In this paper we investigate the “area blow-up” set of a sequence of smooth co-dimension one manifolds whose first variation with respect to an anisotropic integral is bounded. Following the ideas introduced by White in [12], we show that this set has bounded (anisotropic) mean curvature in the viscosity sense. In particular, this allows to show that the set is empty in a variety of situations. As a consequence, we show boundary curvature estimates for two dimensional stable anisotropic minimal surfaces, extending the results of [10].

Original languageEnglish (US)
Pages (from-to)7031-7056
Number of pages26
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume39
Issue number12
DOIs
StatePublished - 2019

Keywords

  • Anisotropic energies
  • Curvature estimates
  • Geometric analysis
  • Minimal surfaces
  • Viscosity solutions

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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