As on arXiv
Abstract
The Ricci flow is one of the most important topics in differential geometry, and a central focus of modern geometric analysis. In this paper, we give an illustrated introduction to the subject which is intended for a general audience. The goal is to provide a working definition of the Ricci flow as well as some intuition for its behavior without assuming any prerequisite knowledge of differential geometry or topology.
Comments: 42 pages, 22 figures
Its neighbourhood
Connected papers
The 6 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Global Analysis: An Introduction to Nonlinear Analysis and Its Variational Methods on Riemannian Manifolds
Topics Ricci flow · Shared terms “introduction”, “differential geometry”, “intended”
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Log-Concavity and Fundamental Gaps on Surfaces of Positive Curvature
Topics Ricci flow · Same author Gabriel Khan
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Extensions and Applications of Bredon's Trick in Geometric and Topological Contexts
Topics Ricci flow · Shared terms “differential geometry”, “geometric analysis”
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Curvature-Torsion Entropy for Twisted Curves under Curve Shortening Flow
Same author Gabriel Khan
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Characterization of Sasakian Manifolds by Curvature Conditions
Topics Ricci flow · Shared terms “differential geometry”
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Courant Algebroid Relations, T-Dualities and Generalised Ricci Flow
Topics Ricci flow · Shared terms “illustrated”, “definition”
Read around it
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
- 5A.5Uniformization and the Two-Dimensional Ricci Flow
Constant-curvature metrics on surfaces, and Ricci flow as a heat equation for the conformal factor.
- 10A.12Curve Shortening and Minimal Discs
How loops shrink under curvature, how the discs they bound lose area, and Perelman's extinction estimate.
- 11A.1The Equation and Its First Solutions
A heat equation for the metric: spheres, cylinders and scaling.