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manuscripta mathematica

, Volume 159, Issue 3–4, pp 453–473 | Cite as

Evolution of the Steklov eigenvalue under geodesic curvature flow

  • Pak Tung HoEmail author
  • Hyunmo Koo
Article
  • 57 Downloads

Abstract

On a two-dimensional compact Riemannian manifold with boundary, we prove that the first nonzero Steklov eigenvalue is nondecreasing along the unnormalized geodesic curvature flow if the initial metric has positive geodesic curvature and vanishing Gaussian curvature. Using the normalized geodesic curvature flow, we also obtain some estimate for the first nonzero Steklov eigenvalue. On the other hand, we prove that the compact soliton of the geodesic curvature flow must be the trivial one.

Mathematics Subject Classification

53C44 58C40 58J50 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsSogang UniversitySeoulKorea

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