Paper · Mar 28, 2022
On Euler characteristic and Hitchin-Thorpe inequality for four-dimensional compact Ricci solitons
As on arXiv
Abstract
In this article, we investigate the geometry of -dimensional compact gradient Ricci solitons. We prove that, under an upper bound condition on the range of the potential function, a -dimensional compact gradient Ricci soliton must satisfy the classical Hitchin-Thorpe inequality. In addition, some volume estimates are also obtained.
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Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 11B.1Ricci Solitons
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
- 12B.2The Asymptotic Soliton and Three-Dimensional Shrinkers
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.