|
|||||
 |
|
|
|
|
|
|
|
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 |
|
| © 2011 MSP (Mathematical Sciences Publishers). |
