A Proof of a General Isoperimetric Inequality for Surfaces

João Lucas Barbosa and Manfredo do Carmo
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João Lucas Barbosa: Universidade Federal Ceara
Manfredo do Carmo: Instituto de Matematica Pura e Applicada

A chapter in Manfredo P. do Carmo – Selected Papers, 2012, pp 145-161 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-25588-5_13

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DOI: 10.1007/978-3-642-25588-5_13

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