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Isoperimetric Inequalities on Surfaces of Constant Curvature

Published online by Cambridge University Press:  20 November 2018

Hsu-Tung Ku ,
Mei-Chin Ku  and
Xin-Min Zhang
Hsu-Tung Ku
Affiliation:
Department of Mathematics and Statistics University of Massachusetts Amherst, MA U.S.A.
Mei-Chin Ku
Affiliation:
Department of Mathematics and Statistics University of South Alabama Mobile, AL U.S.A.
Xin-Min Zhang
Affiliation:
Department of Mathematics and Statistics University of South Alabama Mobile, AL U.S.A.
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Abstract

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In this paper we introduce the concepts of hyperbolic and elliptic areas and prove uncountably many new geometric isoperimetric inequalities on the surfaces of constant curvature.

Keywords

51M1051M2552A4053C20Gaussian curvatureGauss-Bonnet theorempolygon, pseudo-polygonpseudoperimeterhyperbolic surfaceHeron’s formulaanalytic and geometric isoperimetric inequalities
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 6 , 01 December 1997 , pp. 1162 - 1187
Copyright
Copyright © Canadian Mathematical Society 1997

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