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arXiv · 1901.06277

Eigenvalue estimates without Bakry-Emery-Ricci bounds

Gabriel Khan
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Abstract

We establish a lower bound for the real eigenvalues of a Laplace-Beltrami operator with an $L^\infty$-drift term. We make no assumptions that the operator is self-adjoint or that the drift has any additional regularity. In the case where the operator is self-adjoint, this establishes a lower bound on the spectrum without assuming a lower bound for the Bakry-Emery Ricci tensor. Put colloquially, this result states that no matter which way the wind blows, heat will diffuse at a definite rate depending only on the geometry of the underlying space and the maximal wind speed.

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Gabriel Khan. 2019-01-17. Eigenvalue estimates without Bakry-Emery-Ricci bounds. https://arxiv.org/abs/1901.06277

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