Skip to main content
SpringerLink
Log in

Infinitesimal Ricci flows of minimal surfaces in the three-dimensional Euclidean space

  • Published:
Russian Mathematics Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. B. Chow and D. Knopf, The Ricci Flow: An Introduction (Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2004) 110.

    MATH  Google Scholar 

  2. B. Chow, Sun-Chin Chu, Chia-Yi, D. Glickenstein, Ch. Guenther, J. Isenberg, T. Ivey, D. Knopf, P. Lu, F. Luo, and Lei Ni, The Ricci Flow: Techniques and Applications. Part I: Geometric aspects (Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2007) 135.

    MATH  Google Scholar 

  3. Zhu Xi-Ping, Lectures on Mean Curvature Flows (AMS/IP Studies in Advanced Mathematics-32, Providence, RI: American Mathematical Society; Somerville: International Press. ix, 2002).

    MATH  Google Scholar 

  4. B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Modern Geometry. Methods and Applications (Moscow, Nauka, 1979) [in Russian].

    Google Scholar 

  5. M. E. Taylor, Partial Differential Equations. III Nonlinear equations (Springer-Verlag, 1996).

  6. S. A. Carstea and M. Visinescu, “Special Solutions for Ricci Flow Equation in 2D Using the Linearization Approach,” Mod. Phys. Lett. A 20, 39, 2993–3002 (2005) (see also http://arxiv.org/abs/hep-th/0506113).

    Article  MathSciNet  Google Scholar 

  7. R. S. Hamilton, “Three-Manifolds with Positive Ricci Curvature,” J. Differential Geom. 17(2), 255–306, (1982).

    MATH  MathSciNet  Google Scholar 

  8. D. M. DeTurck, “Deforming Metrics in the Direction of their Ricci Tensor,” J. Differential Geom. 18(1), 157–162 (1983).

    MATH  MathSciNet  Google Scholar 

  9. V. F. Kagan, Foundations of the Theory of Surfaces in a Tensor Exposition. Part 1. Technique of Investigation, General Foundations of the Theory, and Intrinsic Geometry of Surfaces (Moscow-Leningrad, 1947) [in Russian].

  10. A. P. Norden, Theory of Surfaces (Moscow, Gostekhizdat, 1956) [in Russian].

    Google Scholar 

  11. J. Rubinstein and R. Sinclair, “Visualizing Ricci Flow of Manifolds of Revolution,” Experimental Mathematics 1, 285–298 (2005).

    MathSciNet  Google Scholar 

  12. V. T. Fomenko, “A Property of Conformal Infinitesimal Deformations of Multidimensional Surfaces in Riemannian Space,” Mat. Zametki 59(2), 284–290 (1996).

    MathSciNet  Google Scholar 

  13. V. T. Fomenko, “An Analog of the Sauer Theorem,” Math. Notes 74(3), 438–444 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  14. W. Blaschke, Introduction to Differential Geometry (Moscow, Gostekhizdat, 1957) [in Russian].

    Google Scholar 

  15. R. S. Palais and Terng Chuu-lian, Critical Point Theory and Submanifold Geometry (Lecture Notes in Math., 1988) 1353.

Download references

Author information

Authors and Affiliations

  1. Universidad de los Andes, Carrera, 1 N 18A 10, Bogotá, Colombia

    J. R. Arteaga

  2. Kazan State University, ul. Kremlyovskaya 18, Kazan, 420008, Russia

    M. A. Malakhaltsev

Authors
  1. J. R. Arteaga
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. A. Malakhaltsev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. R. Arteaga.

Additional information

Original Russian Text © J.R. Arteaga, M.A. Malakhaltsev, 2007, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2007, No. 10, pp. 29–39.

About this article

Cite this article

Arteaga, J.R., Malakhaltsev, M.A. Infinitesimal Ricci flows of minimal surfaces in the three-dimensional Euclidean space. Russ Math. 51, 29–38 (2007). https://doi.org/10.3103/S1066369X07100027

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X07100027

Keywords

Search

Navigation