Heat Kernels Estimates for Hermitian Line Bundles on Manifolds of Bounded Geometry
Keyword(s):
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.
1998 ◽
Vol 58
(2)
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pp. 213-221
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1994 ◽
Vol 74
(1)
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pp. 107-128
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1999 ◽
Vol 6
(2)
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pp. 207-225
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2018 ◽
Vol 468
(2)
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pp. 839-864
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2021 ◽
Vol 86
(2)
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pp. 101-106
Keyword(s):