manuscripta mathematica

, Volume 87, Issue 1, pp 311–325

A generalization of Steiner symmetrization for immersed surfaces and its applications

  • Miyuki Koiso
Article

DOI: 10.1007/BF02570477

Cite this article as:
Koiso, M. Manuscripta Math (1995) 87: 311. doi:10.1007/BF02570477

Abstract

We generalize the classical Steiner symmetrization to surfaces with self-intersections. Then we apply the generalized Steiner symmetrization to several isoperimetric problems. For example, let Г⊂ℝ3 be an analytic plane Jordan curve which is symmetric with respect to a plane ϖ (ϖ⊅Г). LetS be a compact immersed surface bounded by Λ which has the smallest area among all compact surfaces bounded by Λ with a fixed volume. In this situation, under some additional assumptions, the wholeS is proved to be symmetric with respect to ϖ. When Λ is a round circle,S is proved to be a spherical cap or the flat disk bounded by Λ without any additional assumptions.

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Miyuki Koiso
    • 1
  1. 1.Department of MathematicsOsaka UniversityToyonaka, OsakaJapan

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