Heat trace asymptotics with singular weight functions

TL;DR

This paper investigates the asymptotic behavior of the heat trace for Laplace-type operators with boundary conditions, focusing on cases where the weight function has singularities, and provides formulas involving geometric data.

Contribution

It introduces formulas for heat trace asymptotics with singular weight functions, extending previous results to include radial blowup cases.

Findings

Derived explicit formulas for initial terms in the asymptotic expansion.

Connected asymptotic terms to geometric properties of the manifold.

Extended understanding of heat trace behavior with singular weights.

Abstract

We study the weighted heat trace asymptotics of an operator of Laplace type with Dirichlet boundary conditions where the weight function exhibits radial blowup. We give formulas for the first few terms in the expansion in terms of geometrical data.