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arXiv · 2106.10825

Reflecting brownian motion and the gauss-bonnet-chern theorem

Weitao Du·Elton P. Hsu
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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.

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Weitao Du, Elton P. Hsu. 2021-06-21. Reflecting brownian motion and the gauss-bonnet-chern theorem. https://arxiv.org/abs/2106.10825

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