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.
Citation
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
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