Steklov Eigenvalues and Quasiconformal Maps of Simply Connected Planar Domains

A. Girouard, R. S. Laugesen, B. A. Siudeja

Research output: Contribution to journalArticlepeer-review


We investigate isoperimetric upper bounds for sums of consecutive Steklov eigenvalues of planar domains. The normalization involves the perimeter and scale-invariant geometric factors which measure deviation of the domain from roundness. We prove sharp upper bounds for both starlike and simply connected domains for a large collection of spectral functionals including partial sums of the zeta function and heat trace. The proofs rely on a special class of quasiconformal mappings.

Original languageEnglish (US)
Pages (from-to)903-936
Number of pages34
JournalArchive for Rational Mechanics and Analysis
Issue number2
StatePublished - Feb 1 2016

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering


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