Sharp stability inequalities for the plateau problem

G. De Philippis, F. Maggi

Research output: Contribution to journalArticle

Abstract

The validity of global quadratic stability inequalities for uniquely regular area minimizing hypersurfaces is proved to be equivalent to the uniform positivity of the second variation of the area. Concerning singular area minimizing hypersurfaces, by a "quantitative calibration" argument we prove quadratic stability inequalities with explicit constants for all the Lawson's cones, excluding six exceptional cases. As a by-product of these results, explicit lower bounds for the first eigenvalues of the second variation of the area on these cones are derived.

Original languageEnglish (US)
Pages (from-to)399-456
Number of pages58
JournalJournal of Differential Geometry
Volume96
Issue number3
DOIs
StatePublished - Mar 2014

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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