Reflecting brownian motion and the gauss-bonnet-chern theorem (2106.10825v1)

Published 21 Jun 2021 in math.PR

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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