Spectral geometry on manifolds with fibred boundary metrics II: heat kernel asymptotics

2021/01/21 by Mohammad Sadegh Talebi, Talebi, Mohammad, Boris Vertman +1 · 1 citation
Mathematics · #58J52 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2101.08844

openalex publication_date 2021/01/21 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

In this paper we continue the analysis of spectral problems in the setting of complete manifolds with fibred boundary metrics, also referred to as ϕ-metrics, as initiated in our previous work. We consider the Hodge Laplacian for a ϕ-metric and construct the corresponding heat kernel as a polyhomogeneous conormal distribution on an appropriate manifold with corners. Our discussion is a generalization of an earlier work by Albin and Sher, and provides a fundamental first step towards analysis of Ray-Singer torsion, eta-invariants and index theorems in the setting.

Cited by

• Analysis on fibred cusp spaces

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