Curvature, sphere theorems, and the Ricci flow

S. Brendle; R. M. Schoen

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arXiv · 1001.2278

Curvature, sphere theorems, and the Ricci flow

S. Brendle·R. M. Schoen

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Abstract

This is a survey paper focusing on the interplay between the curvature and topology of a Riemannian manifold. The first part of the paper provides a background discussion, aimed at non-experts, of Hopf's pinching problem and the Sphere Theorem. In the second part, we sketch the proof of the Differentiable Sphere Theorem, and discuss various related results. These results employ a variety of methods, including geodesic and minimal surface techniques as well as Hamilton's Ricci flow.

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BibTeX RIS

S. Brendle, R. M. Schoen. 2010-05-31. Curvature, sphere theorems, and the Ricci flow. https://arxiv.org/abs/1001.2278

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