Applications of the 'Ham Sandwich Theorem' to Eigenvalues of the Laplacian

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Abstract

We apply Gromov's ham sandwich method to get: (1) domain monotonicity (up to a multiplicative constant factor); (2) reverse domain monotonicity (up to a multiplicative constant factor); and (3) universal inequalities for Neumann eigenvalues of the Laplacian on bounded convex domains in Euclidean space.

Original languageEnglish
Pages (from-to)317-325
Number of pages9
JournalAnalysis and Geometry in Metric Spaces
Volume4
Issue number1
DOIs
Publication statusPublished - 2016

Keywords

  • Eigenvalues of the Laplacian
  • Ham Sandwich Theorem
  • convexity

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Applied Mathematics

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