Heat trace expansion on manifolds with conic singularities

TL;DR

This paper derives a detailed asymptotic expansion of the heat trace for the Laplace-Beltrami operator on manifolds with conic singularities, providing a foundation for understanding geometric influences on heat behavior.

Contribution

It introduces a precise asymptotic expansion of the heat trace on conic manifolds using the Singular Asymptotics Lemma, advancing spectral geometry analysis.

Findings

Asymptotic expansion of heat trace derived

Expansion reflects geometric features of conic manifolds

Framework sets stage for geometric interpretation in follow-up work

Abstract

We derive a detailed asymptotic expansion of the heat trace for the Laplace-Beltrami operator on functions on manifolds with conic singularities, using the Singular Asymptotics Lemma of Jochen Bruening and Robert T. Seeley [BS]. In the subsequent paper we investigate how the terms in the expansion reflect the geometry of the manifold.