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2011 The Gauss–Bonnet formula on surfaces with densities
Ivan Corwin, Frank Morgan
Involve 4(2): 199-202 (2011). DOI: 10.2140/involve.2011.4.199

Abstract

The celebrated Gauss–Bonnet formula has a nice generalization to surfaces with densities, in which both arclength and area are weighted by positive functions. Surfaces with densities, especially when arclength and area are weighted by the same factor, appear throughout mathematics, including probability theory and Perelman’s recent proof of the Poincaré conjecture.

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Ivan Corwin. Frank Morgan. "The Gauss–Bonnet formula on surfaces with densities." Involve 4 (2) 199 - 202, 2011. https://doi.org/10.2140/involve.2011.4.199

Information

Received: 30 June 2011; Revised: 11 July 2011; Accepted: 11 July 2011; Published: 2011
First available in Project Euclid: 20 December 2017

zbMATH: 1251.53002
MathSciNet: MR2876199
Digital Object Identifier: 10.2140/involve.2011.4.199

Subjects:
Primary: 53B20

Keywords: Density, Gauss–Bonnet

Rights: Copyright © 2011 Mathematical Sciences Publishers

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