Reflecting brownian motion and the gauss-bonnet-chern theorem

2021/06/21 by Weitao Du, Du, Weitao, Elton P. Hsu +1 · 1 citation
Mathematics · Computer Science · #Geometric Analysis and Curvature Flows #Topological and Geometric Data Analysis #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2106.10825

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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