Download this article
 Download this article For screen
For printing
Recent Issues

Volume 17
Issue 4, 543–722
Issue 3, 363–541
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-4184 (online)
ISSN 1944-4176 (print)
 
Author index
To appear
 
Other MSP journals
The Gauss–Bonnet formula on surfaces with densities

Ivan Corwin and Frank Morgan

Vol. 4 (2011), No. 2, 199–202
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.

Keywords
Gauss–Bonnet, density
Mathematical Subject Classification 2010
Primary: 53B20
Milestones
Received: 30 June 2011
Revised: 11 July 2011
Accepted: 11 July 2011
Published: 17 January 2012

Communicated by Michael Dorff
Authors
Ivan Corwin
Courant Institute of Mathematics
New York University
251 Mercer Street
New York, NY 10012
United States
Frank Morgan
Department of Mathematics and Statistics
Williams College
18 Hoxsey Street
Williamstown, MA 01267
United States