## 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}⊂ℝ^{3} 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 language | English |
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Pages (from-to) | 311-325 |

Number of pages | 15 |

Journal | Manuscripta Mathematica |

Volume | 87 |

Issue number | 1 |

DOIs | |

Publication status | Published - Dec 1 1995 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)