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Curvature terms in small time heat kernel expansion for a model class of hypoelliptic Hörmander operators

TitleCurvature terms in small time heat kernel expansion for a model class of hypoelliptic Hörmander operators
Publication TypeJournal Article
Year of Publication2017
AuthorsBarilari, D, Paoli, E
JournalNonlinear Analysis
Volume164
Pagination118 - 134
ISSN0362-546X
KeywordsCurvature; Hypoelliptic heat equation; Small time asymptotics
Abstract

We consider the heat equation associated with a class of second order hypoelliptic Hörmander operators with constant second order term and linear drift. We completely describe the small time heat kernel expansions on the diagonal giving a geometric characterization of the coefficients in terms of the divergence of the drift field and the curvature-like invariants of the optimal control problem associated with the diffusion operator.

URLhttp://www.sciencedirect.com/science/article/pii/S0362546X17302298
DOI10.1016/j.na.2017.09.002

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