A stochastic approach to the Poincaré-Hopf theorem
type: Item
instance of: scholarly article
title: A stochastic approach to the Poincaré-Hopf theorem
zbMATH Open document ID: 0661.58035
DOI: 10.1007/BF00354764
author: Naomasa Ueki
publication date: 1989-01-01T00:00:00Z
review text: The Poincaré-Hopf theorem is proved here by a probabilistic method. The proof of this theorem is reduced to an estimate of a supertrace of the fundamental solution. We use the Malliavin calculus to estimate the fundamental solution. Our proof can be applied to the case that the zero point set is the union of the submanifolds under some conditions.
Mathematics Subject Classification ID: 58J65
zbMATH DE Number: 4080465
zbMATH Keywords: Poincaré-Hopf theorem
zbMATH Keywords: supertrace
zbMATH Keywords: Malliavin calculus
zbMATH Keywords: fundamental solution
MaRDI profile type: Publication
cites work: A Lefschetz fixed point formula for elliptic complexes. II: Applications
cites work: The Atiyah-Singer theorems: A probabilistic approach. I: The index theorem
cites work: The Witten complex and the degenerate Morse inequalities
cites work: Q3756011
cites work: Fixed point index and fixed point theorem for Euclidean neighborhood retracts
cites work: Q3679959
cites work: Q4134602
cites work: Q3959169
cites work: Q3753202
cites work: Q5731354
cites work: Q5510566
cites work: Q4064108
cites work: Lectures on stochastic differential equations and Malliavin calculus
cites work: Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels
cites work: Q3768095
cites work: Supersymmetry and Morse theory
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4080465