A generalization of Steiner symmetrization for immersed surfaces and its applications

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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 G{cyrillic}⊂ℝ3 be an analytic plane Jordan curve which is symmetric with respect to a plane π{variant} (π{variant}⊅G{cyrillic}). Let S 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 whole S is proved to be symmetric with respect to π{variant}. 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.

Original languageEnglish
Pages (from-to)311-325
Number of pages15
JournalManuscripta Mathematica
Volume87
Issue number1
DOIs
Publication statusPublished - Dec 1 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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