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arXiv · 1810.12205

Bounds on the first Betti number - an approach via Schatten norm estimates on semigroup differences

Marcel Hansmann·Christian Rose·Peter Stollmann
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Abstract

We derive new estimates for the first Betti number of compact Riemannian manifolds. Our approach relies on the Birman-Schwinger principle and Schatten norm estimates for semigroup differences. In contrast to previous works we do not require any a priori ultracontractivity estimates and we provide bounds which explicitly depend on suitable integral norms of the Ricci tensor.

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BibTeXRIS

Marcel Hansmann, Christian Rose, Peter Stollmann. 2018-10-29. Bounds on the first Betti number - an approach via Schatten norm estimates on semigroup differences. https://arxiv.org/abs/1810.12205

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