Gaussian heat kernel estimates: from functions to forms

Thierry Coulhon*, Baptiste Devyver, Adam Sikora

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review


    On a complete non-compact Riemannian manifold satisfying the volume doubling property, we give conditions on the negative part of the Ricci curvature that ensure that, unless there are harmonic 1-forms, the Gaussian heat kernel upper estimate on functions transfers to one-forms. These conditions do no entail any constraint on the size of the Ricci curvature, only on its decay at infinity.

    Original languageEnglish
    Pages (from-to)25-79
    Number of pages55
    JournalJournal fur die Reine und Angewandte Mathematik
    Issue number761
    Early online date5 Oct 2018
    Publication statusPublished - Apr 2020


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