A probabilistic proof of the Gauss-Bonnet-Chern theorem for manifolds with boundary
type: Item
instance of: scholarly article
title: A probabilistic proof of the Gauss-Bonnet-Chern theorem for manifolds with boundary
zbMATH Open document ID: 0704.58056
author: Ichiro Shigekawa
author: Naomasa Ueki
author: Shinzo Watanabe
published in: Osaka Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The authors prove the Gauß-Bonnet-Chern theorem for a manifold with boundary by a probabilistic method. To construct the fundamental solution of the heat equation they adopt a probabilistic approach to the initial value problem due to Airault and Ikeda-Watanabe. Then they combine this result with a modified Malliavin calculus and obtain that the fundamental solution can still be expressed as a generalized Wiener functional expectation. Evaluating probabilistically the short time behaviour of this generalized expectation they can directly compute the Gauß- Bonnet-Chern theorem.
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 58J35
Mathematics Subject Classification ID: 58J32
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 4155531
zbMATH Keywords: Gauß-Bonnet-Chern theorem
zbMATH Keywords: fundamental solution of the heat equation
zbMATH Keywords: generalized Wiener functional
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4155531