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.

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

Barilari D.;
2017

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3368981
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