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

Author

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  • Yuri A. Kordyukov

    (Institute of Mathematics, Ufa Federal Research Center, Russian Academy of Sciences, 450008 Ufa, Russia)

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.

Suggested Citation

  • Yuri A. Kordyukov, 2021. "Heat Kernels Estimates for Hermitian Line Bundles on Manifolds of Bounded Geometry," Mathematics, MDPI, vol. 9(23), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3060-:d:690233
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