Geometric Flows
Ricci flow, mean curvature flow, and harmonic map heat flow.
Geometric Flows. Ricci flow, mean curvature flow, and harmonic map heat flow.
Foundations and canonical references
The standard treatments of geometric flows approach the subject from complementary angles. Chow, The Ricci Flow: An Introduction (2004) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Supporting and adjacent work
A number of supporting contributions sharpen specific aspects of geometric flows or connect it to neighbouring problems. The entropy formula for the Ricci flow and its geometric applications (Perelman, 2002) contributes to this area as one of the supporting references that inform current practice.
Open methodological questions for geometric flows include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2004The Ricci Flow: An Introductionchow-2004, knopf-2004
- paper · historical · 2002perelman-2002
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