An isoperimetric inequality for the harmonic mean of the Steklov eigenvalues in hyperbolic space

Abstract

In this article, we prove an isoperimetric inequality for the harmonic mean of the first \((n-1)\) nonzero Steklov eigenvalues on bounded domains in n-dimensional hyperbolic space. Our approach to prove this result also gives a similar inequality for the first n nonzero Steklov eigenvalues on bounded domains in n-dimensional Euclidean space.

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Correspondence to Sheela Verma.

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Verma, S. An isoperimetric inequality for the harmonic mean of the Steklov eigenvalues in hyperbolic space. Arch. Math. 116, 193–201 (2021). https://doi.org/10.1007/s00013-020-01549-x

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Keywords

  • Isoperimetric inequality
  • Steklov eigenvalue problem
  • Exponential map
  • Geodesic normal coordinate system

Mathematics Subject Classification

  • Primary 35P15
  • Secondary 58J50