Stronger Radial Attraction: A Generalization of Radial Curvature bounded from above

TL;DR

This paper generalizes the concept of radial curvature bounds in Riemannian geometry, extending the classical notion to broader contexts and providing new insights into geometric comparison theorems.

Contribution

It introduces a new generalized framework for radial curvature bounds, expanding the applicability of comparison geometry techniques.

Findings

New generalized radial curvature bounds established

Comparison theorems extended to broader classes of manifolds

Potential applications in geometric analysis and topology

Abstract

This paper introduces and investigates a generalization of the notion of a pointed Riemannian manifold having its radial curvature bounded from above by that of a model surface of revolution.