Willmore blowups are never compact

Duke Mathematical Journal

Volumn 147, Issue 2, 2009, Pages 345-376

  Chill, Ralph ^a   Fašangová, Eva ^a   Schätzle, Reiner ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70449640961     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/00127094-2009-014     Document Type: Article

References (18)

1. S. B. Angenent, Nonlinear analytic semiflows, Proc. Roy. Soc. Edinburgh Sect. A 115 (1990), 91-107. Mathematical Reviews (MathSciNet): MR1059647 Zentralblatt MATH: 0723.34047
2. S. Blatt, Beispiel eines blowup-limes für den Willmorefluss, diploma thesis, Universität Bonn, Bonn, Germany, 2004
3. R. Chill, On the Łojasiewicz-Simon gradient inequality, J. Funct. Anal. 201 (2003), 572-601. Mathematical Reviews (MathSciNet): MR1986700 Digital Object Identifier: doi:10.1016/S0022-1236(02)00102-7
4. E. Kuwert and R. SchäTzle, The Willmore flow with small initial energy, J. Differential Geom. 57 (2001), 409-441. Mathematical Reviews (MathSciNet): MR1882663 Project Euclid: euclid.jdg/1090348128 Zentralblatt MATH: 1035.53092
5. E. Kuwert and R. SchäTzle, Gradient flow for the Willmore functional, Comm. Anal. Geom. 10 (2002), 307-339. Mathematical Reviews (MathSciNet): MR1900754 Zentralblatt MATH: 1029.53082
6. E. Kuwert and R. SchäTzle, Removability of point singularities of Willmore surfaces, Ann. of Math. (2) 160 (2004), 315-357. Mathematical Reviews (MathSciNet): MR2119722 Digital Object Identifier: doi:10.4007/annals.2004.160.315 Zentralblatt MATH: 1078.53007
7. O. A. Ladyženskaja, v. a. solonnikov, and N. N. Ural'Ceva, Linear and Quasilinear Equations of Parabolic Type, English translation in Trans. Math. Monogr. 23, Amer. Math. Soc., Providence, 1967. Mathematical Reviews (MathSciNet): MR0241822
8. p-bounded second fundamental form, Math. Ann. 270 (1985), 223-234. Mathematical Reviews (MathSciNet): MR0771980 Digital Object Identifier: doi:10.1007/BF01456183 Zentralblatt MATH: 0564.58010
9. P. Li and S.T. Yau, A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces, Invent. Math. 69 (1982), 269-291. Mathematical Reviews (MathSciNet): MR0674407 Digital Object Identifier: doi:10.1007/BF01399507 Zentralblatt MATH: 0503.53042
10. S. łOjasiewicz, Ensembles semi-analytiques, preprint, Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France, 1965.
11. A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Progr. Nonlinear Differential Equations Appl. 16, Birkhäuser, Basel, 1995. Mathematical Reviews (MathSciNet): MR1329547 Zentralblatt MATH: 0816.35001
12. U. F. Mayer and G. Simonett, A numerical scheme for axisymmetric solutions of curvature-driven free boundary problems, with applications to the Willmore flow, Interfaces Free Bound. 4 (2002), 89-109. Mathematical Reviews (MathSciNet): MR1877537
13. L. Simon, Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems, Ann. of Math. (2) 118 (1983), 525-571. Mathematical Reviews (MathSciNet): MR0727703 Digital Object Identifier: doi:10.2307/2006981 JSTOR: links.jstor.org
14. G. Simonett, The Willmore flow near spheres, Differential Integral Equations 14 (2001), 1005-1014. Mathematical Reviews (MathSciNet): MR1827100
15. J. Simons, Minimal varieties in riemannian manifolds, Ann. of Math. (2) 88 (1968), 62-105. Mathematical Reviews (MathSciNet): MR0233295 Digital Object Identifier: doi:10.2307/1970556 JSTOR: links.jstor.org
16. T. J. Willmore, Total Curvature in Riemannian Geometry, Ellis Horwood Ser. Math. Appl., Wiley, New York, 1982. Mathematical Reviews (MathSciNet): MR0686105 Zentralblatt MATH: 0501.53038
17. T. J. Willmore, Riemannian Geometry, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993. Mathematical Reviews (MathSciNet): MR1261641
18. E. Zeidler, Nonlinear Functional Analysis and Its Applications, I: Fixed-Point Theorems, Springer, New York, 1986. Mathematical Reviews (MathSciNet): MR0816732 Zentralblatt MATH: 0583.47050