Reflecting brownian motion and the gauss-bonnet-chern theorem
Probability
2021-06-22 v1
Abstract
We use reflecting Brownian motion (RBM) to prove the well known Gauss-Bonnet-Chern theorem for a compact Riemannian manifold with boundary. The boundary integrand is obtained by carefully analyzing the asymptotic behavior of the boundary local time of RBM for small times.
Keywords
Cite
@article{arxiv.2106.10825,
title = {Reflecting brownian motion and the gauss-bonnet-chern theorem},
author = {Weitao Du and Elton P. Hsu},
journal= {arXiv preprint arXiv:2106.10825},
year = {2021}
}