Geometry and topology of manifolds with integral radial curvature bounds

TL;DR

This paper explores how integral bounds on radial curvature influence the geometric and topological properties of manifolds, providing new insights into their structure.

Contribution

It introduces novel results connecting integral radial curvature bounds with manifold geometry and topology, extending previous curvature comparison theories.

Findings

Derived new topological classifications under integral curvature bounds

Established geometric inequalities related to radial curvature

Provided examples illustrating the sharpness of results

Abstract

In this paper, we systematically investigate the geometry and topology of manifolds with integral radial curvature bounds, and obtain many interesting and important conclusions.