Heat kernel expansions in vector bundles

DOI10.1016/J.NA.2008.11.085zbMath1238.58015OpenAlexW2061978985MaRDI QIDQ419784

Martin Ngu Ndumu

Publication date: 20 May 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2008.11.085

zbMATH Keywords

Riemannian manifoldcurvatureexponential mapgeodesicheat kernelvector bundlenormal coordinatesexpansion coefficientscurvature formBrownian Riemannian bridge processconnection formLaplace-type operatornormal neighborhood

Mathematics Subject Classification ID

Diffusion processes and stochastic analysis on manifolds (58J65) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Perturbations of PDEs on manifolds; asymptotics (58J37) Heat kernel (35K08) PDEs on manifolds (35R01)

Related Items (1)

First order Feynman-Kac formula

Cites Work

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• Riemannian geometry as determined by the volumes of small geodesic balls
• Comparison theorems for the volumes of tubes as generalizations of the Weyl tube formula
• The volume of a small geodesic ball of a Riemannian manifold
• An integral formula for the heat kernel of tubular neighborhoods of complete (connected) Riemannian manifolds
• Curvature and spectrum of Riemannian manifold
• Curvature and the eigenvalues of the Laplacian
• On eigen-values of Laplacian and curvature of Riemannian manifold
• Behavior of diffusion semi-groups at infinity
• Characteristic Classes. (AM-76)
• Heat equation derivative formulas for vector bundles
• Riemannian geometry and geometric analysis

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