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arXiv · 1904.08595

Quantitative comparison theorems in Riemannian and Kähler geometry

Kwok-Kun Kwong
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Abstract

We obtain sharp quantitative Laplacian upper and lower estimates under no assumption on curvatures. As a result, we derive quantitative Laplacian, area and volume comparison theorems for tubes in Riemannian and Kähler manifolds under weak integral curvature assumptions. We also give some applications, such as a general Bonnet-Myers theorem and Cheng's eigenvalue estimate under weak integral curvature assumptions.

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BibTeXRIS

Kwok-Kun Kwong. 2019-04-18. Quantitative comparison theorems in Riemannian and Kähler geometry. https://arxiv.org/abs/1904.08595

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