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Surface Topology and Geometry

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Ricci Flow for Shape Analysis and Surface Registration

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Abstract

This chapter briefly reviews the fundamental concepts and theorems in algebraic topology [1], surface differential geometry [6], and surface Ricci flow [4, 7]. Detailed discussion on Ricci flow on general Riemannian manifolds can be found in [5]. Advanced topics on differential geometry related to Yamabe equations can be found in [9].

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References

  1. Armstrong, M.: Basic Topology. Undergraduate Texts in Mathematics. Springer, New York (1983)

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  2. Chern, S.: An elementary proof of the existence of isothermal parameters on a surface. Proc. Am. Math. Soc. 6(5), 771–782 (1955)

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  3. Chern, S.S., Cesari, L.: Global Differential Geometry. Mathematical Association of America, Providence, RI (1989)

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  5. Chow, B., Lu, P., Ni, L.: Hamilton’s Ricci Flow, Graduate Studies in Mathematics, vol. 77. American Mathematical Society, Providence, RI (2006)

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  6. DoCarmo, M.P.: Differential Geometry of Curves and Surfaces, 1st edn. Pearson (1976)

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  7. Hamilton, R.: Ricci flow on surfaces. Mathematics and General Relativity. Contemporary Mathematics, vol. 71, pp. 237–261. AMS, Providence, RI (1988)

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  8. Li, P., Yau, S.T.: On the parabolic kernel of the Schrödinger operator. Acta Math. 156, 153–201 (1986)

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  9. Schoen, R., Yau, S.T.: Lecture on Differential Geometry, vol. 1. International Press Incorporated, Boston (1994)

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Authors and Affiliations

  1. Computing and Information Science, Florida International University, Miami, FL, USA

    Wei Zeng

  2. Computer Science, State University of New York, Stony Brook, NY, USA

    Xianfeng David Gu

Authors
  1. Wei Zeng
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  2. Xianfeng David Gu
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Zeng, W., Gu, X.D. (2013). Surface Topology and Geometry. In: Ricci Flow for Shape Analysis and Surface Registration. SpringerBriefs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8781-4_2

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