Comparison geometry for integral generalized quasi-Einstein tensor bounds
Sanghun Lee
TL;DR
This paper extends classical geometric comparison theorems to integral generalized quasi-Einstein tensors, providing new tools for analyzing geometric properties and deriving a global diameter estimate.
Contribution
It introduces generalized comparison theorems for integral quasi-Einstein tensors and applies them to obtain a global diameter bound.
Findings
Extended mean curvature and volume comparison estimates.
Derived a global diameter estimate.
Enhanced understanding of geometric bounds for quasi-Einstein structures.
Abstract
The purpose of this paper is to extend the mean curvature comparison and volume comparison estimates by Petersen, Sprouse, and Wei to integral generalized quasi-Einstein tensor. Moreover, we use our comparison results to get global diameter estimate.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Elasticity and Material Modeling · Advanced Differential Geometry Research