Geometry of Complete Gradient Shrinking Ricci Solitons
Huai-Dong Cao
TL;DR
This paper reviews recent advances in the geometry of complete gradient shrinking Ricci solitons, focusing on classification in three dimensions, asymptotic behavior of potential functions, and volume growth in higher dimensions.
Contribution
It provides a comprehensive survey of recent progress on the classification and geometric properties of complete gradient shrinking Ricci solitons.
Findings
Classification results in three dimensions
Asymptotic behavior of potential functions
Volume growth estimates in higher dimensions
Abstract
We survey some of the recent progress on complete gradient shrinking Ricci solitons, including the classifications in dimension three and asymptotic behavior of potential functions as well as volume growths of geodesic balls in higher dimensions. This article is written for the conference proceedings dedicated to Yau's 60th birthday.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research