A Navier boundary value problem for Willmore surfaces of revolution

Analysis (Germany)

Volumn 29, Issue 3, 2009, Pages 229-258

  Deckelnick, Klaus ^a   Grunau, Hans Christoph ^b  

^a Fakultäml t füml r Mathematik Otto von Guericke Universitäml t Postfach   (Germany)

^b

^c Germany

Author keywords

bifurcation; Clifford torus; natural boundary value problem; Newton's method; surfaces of revolution; Willmore surfaces

Indexed keywords

EID: 84986275189     PISSN: 01744747     EISSN: 21966753     Source Type: Journal    
DOI: 10.1524/anly.2009.1035     Document Type: Article

References (19)

1. M. Bauer, E. Kuwert, Existence of minimizing Willmore surface of prescribed genus, Int. Math. Res. Not. 2003, No. 10, 553-576, 2003.
2. M. G. Crandall, P. H. Rabinowitz, Bifurcation from simple eigenvalues, J. Functional Analysis, 8, 321-340, 1971.
3. A. Dall'Acqua, K. Deckelnick, H.-Ch. Grunau, Classical solutions to the Dirichlet problem for Willmore surfaces of revolution, Adv. Calc. Var., 1, 379-397, 2008.
4. A. Dall'Acqua, S. Fröhlich, H.-Ch. Grunau, F. Schieweck, Symmetric Will-more surfaces of revolution satisfying arbitrary Dirichlet boundary data, Preprint 24-2008, Faculty of Mathematics, University of Magdeburg, 2008.
5. K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin etc., 1985.
6. U. Dierkes, S. Hildebrandt, A. Küster, O. Wohlrab, Minimal Surfaces I, Grundlehren der mathematischen Wissenschaften 295, Springer-Verlag: Berlin etc., 1992.
7. S. Fröhlich, Katenoidähnliche Lösungen geometrischer Variationsprobleme, Preprint 2322, FB Mathematik, TU Darmstadt, 2004.
8. D. Kastsian, Finite element approximation of two-dimensional rotationally symmetric Willmore surfaces, Master thesis, University of Magdeburg, 2007.
9. E. Kuwert, R. Schätzle, Closed surfaces with bounds on their Willmore energy, Preprint, 2008.
10. E. Kuwert, R. Schätzle, Minimizers of the Willmore functional under fixed conformal class, Preprint, 2008.
11. K. Leschke, F. Pedit, U. Pinkall, Willmore tori in the 4-sphere with nontrivial normal bundle, Math. Ann., 332, 381-394, 2005.
12. J. C. C. Nitsche, Boundary value problems for variational integrals involving surface curvatures, Quarterly Appl. Math., 51, 363-387, 1993.
13. S. D. Poisson, Mémoire sur les surfaces élastiques, Cl. Sci. Mathém. Phys. Inst, de France, 2nd printing, 167-225, 1812.
14. T. Rivière, Analysis aspects of Willmore surfaces, Invent. Math., 174, 1-45, 2008.
15. R. Schätzle, The Willmore boundary value problem, Preprint, 2006; to appear in Calculus of Variations and Partial Differential Equations, 2009.
16. M. Schmidt, Existence of minimizing Willmore surfaces of prescribed conformal class, Preprint, arXiv:math/0403301vl, 2004.
17. L. Simon, Existence of surfaces minimizing the Willmore functional, Commun. Anal. Geom., 1, 281-326, 1993.
18. G. Thomsen, Über konforme Geometrie I: Grundlagen der konformen Flächentheorie, Abh. Math. Sem. Univ. Hamburg 3, 31-56, 1923.
19. T. J. Willmore, Riemannian Geometry, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1993.