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A Proof of a General Isoperimetric Inequality for Surfaces

  • João Lucas Barbosa
  • Manfredo do Carmo
Chapter

Abstract

(1.1) Let M be a two-dimensional C2-manifold endowed with a C2-Riemannian metric. We say that M is a generalized surface if the metric in M is allowed to degenerate at isolated points; such points are called singularities of the metric. In this paper we use the method of Fiala-Bol (cf. [12, 9]) to give a proof of the following general isoperimetric inequality.

Keywords

Gaussian Curvature Connected Domain Isoperimetric Inequality Geodesic Curvature Geodesic Disk 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • João Lucas Barbosa
    • 1
  • Manfredo do Carmo
    • 2
  1. 1.Universidade Federal CearaFortaleza-CeBrasil
  2. 2.Instituto de Matematica Pura e ApplicadaRio de JaneiroBrasil

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