Gradient flow for the Willmore functional

Communications in Analysis and Geometry

Volumn 10, Issue 2, 2002, Pages 307-339

  Kuwert, Ernst ^a   Schätzle, Reiner ^b  

^a UNIVERSITY OF FREIBURG   (Germany)

^b UNIVERSITY OF BONN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038779042     PISSN: 10198385     EISSN: None     Source Type: Journal    
DOI: 10.4310/CAG.2002.v10.n2.a4     Document Type: Article

References (14)

1. R. Bryant, A Duality Theorem for Willmore Surfaces, J. Differential Geom., 20 (1984), 23-53.
2. J. Escher, U. Mayer, and G. Simonett, The Surface Diffusion Flow for Immersed Hypersurfaces, Siam. J. Math. Anal., 29(6) (1998), 1419-1433.
3. R. Hamilton, Three-Manifolds with Positive Ricci Curvature, J. Differential Geom., 17 (1982), 255-306.
4. R. Kusner, Estimates for the Biharmonic Energy on Unbounded Planar Domains, and the Existence of Surfaces of Every Genus that Minimize the Squared-Mean-Curvature Integral, in 'Elliptic and Parabolic Methods in Geometry,' AK Peters, 1996.
5. E. Kuwert and R. Schätzle, The Willmore Flow with small initial energy, (2002), to appear in Journal of Differential Geomerty.
6. O.A. Ladyzhenskaya, V.A. Solonnikov, and N.N. Uraltseva, Linear and Quasilinear Equations of Parabolic Type, American Math. Society, 1968.
7. n, Comm. Pure Appl. Math., 26 (1973), 361-379.
8. A. Polden, Closed Curves of Least Total Curvature, Sonderforschungsbereich, 382, Preprint Nr. 13, Tübingen 1995.
9. A. Polden, Curves and Surfaces of Least Total Curvature and Fourth-Order Flows, Dissertation, Universität Tübingen, 1996.
10. L. Simon, Existence of Surfaces Minimizing the Willmore Functional, Commun. Analysis Geom., 1(2) (1993), 281-326.
11. G. Simonett, The Willmore Flow near Spheres, preprint, 1999.
12. M. Struwe, On the Evolution of Harmonic Maps of Riemannian Surfaces, Comment. Math. Helv., 60(2) (1985), 558-581.
13. T. Willmore, Riemannian Geometry, Oxford University Press, New York, 1993.
14. T. Willmore, Note on Embedded Surfaces, An. Stiint. Univ., "Al. I. Cusa" Iasi Sect. Ia, 11B (1965), 493-496.