Heat Kernels Estimates for Hermitian Line Bundles on Manifolds of Bounded Geometry

Yuri A. Kordyukov
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Yuri A. Kordyukov: Institute of Mathematics, Ufa Federal Research Center, Russian Academy of Sciences, 450008 Ufa, Russia

Mathematics, 2021, vol. 9, issue 23, 1-15

Abstract: We consider a family of semiclassically scaled second-order elliptic differential operators on high tensor powers of a Hermitian line bundle (possibly, twisted by an auxiliary Hermitian vector bundle of arbitrary rank) on a Riemannian manifold of bounded geometry. We establish an off-diagonal Gaussian upper bound for the associated heat kernel. The proof is based on some tools from the theory of operator semigroups in a Hilbert space, results on Sobolev spaces adapted to the current setting, and weighted estimates with appropriate exponential weights.

Keywords: heat kernel estimates; manifold of bounded geometry; Bochner Laplacian; elliptic differential operator; Hermitian line bundle; semiclassical asymptotics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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