Quantitative comparison theorems in Riemannian and K\"ahler geometry
Differential Geometry
2019-04-19 v1
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 K\"ahler 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.
Cite
@article{arxiv.1904.08595,
title = {Quantitative comparison theorems in Riemannian and K\"ahler geometry},
author = {Kwok-Kun Kwong},
journal= {arXiv preprint arXiv:1904.08595},
year = {2019}
}
Comments
35 pages, no figure