In this paper we continue with the analysis of spectral problems in the setting of complete manifolds with fibred boundary metrics, also referred to as $$\phi $$ ϕ -metrics, as initiated in our previous work (Grieser et al. in Spectral geometry on manifolds with fibred boundary metrics I: Low energy resolvent, 2020). We consider the Hodge Laplacian for a $$\phi $$ 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.

Spectral geometry on manifolds with fibered boundary metrics I: Low energy resolventTome 9 (2022), p. 959-1019. © Les auteurs, 2022. Certains droits réservés. Cet article est mis à disposition selon les termes de la licence LICENCE INTERNATIONALE D'ATTRIBUTION CREATIVE COMMONS BY 4.0. https://creativecommons.org/licenses/by/4.0/ L'accès aux articles de la revue « Journal de l'École polytechnique -Mathématiques » (http://jep.centre-mersenne.org/), implique l'accord avec les conditions générales d'utilisation (http://jep.centre-mersenne.org/legal/). Publié avec le soutien du Centre National de la Recherche Scientifique Publication membre du Centre Mersenne pour l'édition scientifique ouverte www.centre-mersenne.org