A Proof of a General Isoperimetric Inequality for Surfaces

  • João Lucas Barbosa
  • Manfredo do Carmo
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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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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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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