Quantitative comparison theorems in Riemannian and Kähler geometry

2019/04/18 by Kwok‐Kun Kwong, Kwong, Kwok-Kun
Mathematics · Medicine · #53C23 #53C55 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Pelvic and Acetabular Injuries

paper · pdf · doi:10.48550/arxiv.1904.08595

openalex publication_date 2019/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Differential equations on riemannian manifolds and their geometric applications

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