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Original Article

Visualizing Ricci Flow of Manifolds of Revolution

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Pages 285-298 | Published online: 30 Jan 2011

  • S. Altschuler, S. Angenent, and Y. Giga. "Mean Curvature Flow through Singularities for Surfaces of Revolution." The Journal of Geometric Analysis 5 (1995), 293–358.
  • S. Angenent and D. Knopf. "An Example of Neck Pinching for Ricci Flow on S n+1." Mathematical Research Letters 11 (2004), 493–518.
  • S. Bleiler and C. Hodgson. "Spherical Space Forms and Dehn Filling." Topology 35 (1996), 809–833.
  • G. L. Browning, J. J. Hack, and P. N. Swartztrauber. "A Comparison of Three Numerical Methods for Solving Differential Equations on the Sphere." Monthly Weather Review 117 (1989), 1058–1075.
  • H. Cao, B. Chow, S. Chu, and S. T. Yau, editors. Collected Papers on Ricci Flow, Series in Geometry and Topology, 37. Cambridge, MA: International Press, 2003.
  • D. L. Chopp and J. A. Sethian. "Flow under Curvature: Singularity Formation, Minimal Surfaces, and Geodesics." Experimental Mathematics 2 (1993), 235–255.
  • B. Chow. "The Ricci Flow on the 2-Sphere." In Collected Papers on Ricci Flow, edited by H. Cao et al., 226–237, Series in Geometry and Topology, 37. Cambridge, MA: International Press, 2003.
  • B. Chow and D. Knopf. The Ricci Flow: An Introduction, Mathematical Surveys and Monographs, 110. Providence, RI: Amer. Math. Soc., 2004.
  • M. Engman. "A Note on Isometric Embeddings of Surfaces of Revolution." American Mathematical Monthly 111 (2004), 251–255.
  • D. Garfinkle and J. Isenberg. "Numerical Studies of the Behavior of Ricci Flow." In Contemporary Mathematics, Vol. 367, edited by Shu-Cheng Chang, Bennet Chow, Sun-Chin Chu, and Chang-Shou Lin, 103–114. Providence, RI: American Mathematical Society, 2005.
  • M. Gromov and W. Thurston. "Pinching Constants for Hyperbolic Manifolds." Inventiones Mathematicae 89 (1987), 1–12.
  • A. Heck. Introduction to Maple, Third edition. New York: Springer-Verlag, 2003.
  • T. Ivey. "The Ricci Flow on Radially Symmetric R 3." Communications in Partial Differential Equations 19 (1994), 1481–1500.
  • D. Keene, translator. Essays in Idleness: The Tsurezuregusa of Kenkō. New York: Columbia University Press, 1998.
  • B. W. Kernighan and D. M. Ritchie. The C Programming Language, Second edition. Englewood Cliffs, NJ: Prentice Hall, 1988.
  • D. Knopf. "An Introduction to the Ricci Flow Neckpinch." In Contemporary Mathematics, Vol. 367, edited by Shu-Cheng Chang, Bennet Chow, Sun-Chin Chu, and Chang-Shou Lin, 141–148. Providence, RI: American Mathematical Society, 2005.
  • P. R. A. Leviton and J. H. Rubinstein. "Deforming Riemannian Metrics on the 2- Sphere." In Miniconference on Geometry and Partial Differential Equations (Canberra (1985), edited by L. Simon and N. S. Trudinger, 123–127, Proceedings of the Centre for Mathematical Analysis ANU, 10. Canberra: Australian National University, 1986.
  • G. Perelman. "The Entropy Formula for the Ricci Flow and Its Geometric Applications." arXiv:math.DG/0211159, 2002.
  • G. Perelman. "Ricci Flow with Surgery on Three-Manifolds." arXiv:math.DG/0303109, 2003.
  • J. A. Sethian. Level Set Methods, Cambridge Monographs on Applied and Computational Mathematics, 3. Cambridge, UK: Cambridge University Press, (1996).
  • Dave Shreiner, Mason Woo, Jackie Neider, and Tom Davis. OpenGL Programming Guide, Fourth edition. Reading, MA: Addison-Wesley, (2003).
  • M. Simon. "A Class of Riemannian Manifolds that Pinch when Evolved by Ricci Flow." Manuscripta Mathematica 101 (2000), 89–114.

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