Heat trace asymptotics for wedge-like singularity

TL;DR

This paper investigates the heat trace expansion on manifolds with wedge-like singularities, identifying specific terms that encode geometric information about the singularity.

Contribution

It provides explicit expressions for the logarithmic and half-power terms in the heat trace expansion related to wedge-like singularities.

Findings

Identifies the logarithmic term $ct^{-1/2} ext{log} t$ in the expansion.

Derives a geometric expression for the coefficient $c$.

Shows the presence of a half-power term $bt^{-1/2}$ related to the singularity.

Abstract

In this note we consider a heat trace expansion on a manifold with wedge-like singularity. We show that there are two terms in the expansion that contain information about the presence of the singularity, namely the logarithmic term $ct^{-1/2}\log t$ and the half power term $bt^{-1/2}$. We also give a geometric expression for $c$.