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Ricci Flow Reading Group

Time

Spring 2025, Fridays 3:00-4:00pm

Audience Notes

The following are notes from a reading group on Ricci flow.

Date Topic Speaker Reference
Feb 1 Short-Time Existence and Uniqueness Xinran [She02]
Feb 14 Hamilton’s Existence Theorem Huy [Ham86]
Feb 21 Tame Fréchet Spaces Huy [Ham86]
Feb 28 The Nash-Moser Inverse Function Theorem Huy [Ham86]
Mar 7 Local Invertibility Huy [Ham86]
Mar 14 Higher-Dimension Pinching Estimate 1 Xinran [CLN06, §7.1]
Apr 4 Higher-Dimension Pinching Estimate 2 Xinran [CLN06, §7.1]
Apr 14 Four Manifolds with Positive Curvature
The Maximum Principle on Noncompact Manifolds 1 		Xinran [CLN06, §§7.2-7.4]
Apr 18 The Maximum Principle on Noncompact Manifolds 2 Xinran [CLN06, §§7.4-7.5]
Apr 28 Ricci Flow on Asymptotically Euclidean Manifolds 1 Eric [Li18]
May 2 Ricci Flow on Asymptotically Euclidean Manifolds 2 Huy [Li18]
May 15 Ricci Flow on Asymptotically Euclidean Manifolds 3 Huy [Li18]

References

  1. [She02] Sheridan, A. "Hamilton's Ricci Flow." Mathematical Reviews, vol. 105, no. 6, 2002, pp. 845–860. https://web.math.princeton.edu/~nsher/ricciflow.pdf
  2. [Ham86] Hamilton, R. S. "Three-manifolds with positive Ricci curvature." Journal of Differential Geometry, vol. 17, no. 2, 1986, pp. 255–306. https://projecteuclid.org/euclid.jdg/1214436922
  3. [CLN06] Chow, B., Lu, P., and Ni, L. Hamilton's Ricci Flow. Graduate Studies in Mathematics, vol. 77, American Mathematical Society, 2006. https://bookstore.ams.org/gsm-77/
  4. [Li18] Yu Li. "Ricci flow on asymptotically Euclidean manifolds." Geometry & Topology, vol. 22, no. 4, 2018, pp. 1837–1891. https://doi.org/10.2140/gt.2018.22.1837.