Uniqueness theorems for Willmore surfaces with fixed and free boundaries

Indiana University Mathematics Journal

Volumn 49, Issue 4, 2000, Pages 1581-1601

  Palmer, Bennett ^a  

^a DURHAM UNIVERSITY   (United Kingdom)

Author keywords

Flux formula; Free boundary; Willmore surface

Indexed keywords

EID: 0040214815     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.2000.49.1872     Document Type: Article

References (20)

1. L. ALÍAS, R. LÓPEZ & B. PALMER, Stable constant mean curvature surfaces with circular boundaries, Amer. Math. Soc. Proc. 127 (1999), 1195-2000.
2. M. BABICH & A. BOBENKO, Willmore tori with umbilic lines and minimal surfaces in hyperbolic space, Duke Math. J. 72 (1993), 141-185.
3. R. BRYANT, A duality theorem for Willmore surfaces, J. Differential Geom. 20 (1984), 23-53.
4. R. COURANT & D. HILBERT, Methods of Mathematical Physics, Volume I, John Wiley, New York, 1989.
5. R. EARP, B. BRITO, W.H. MEEKS, H. ROSENBERG, Structure theorems for constant mean curvature surfaces bounded by a planar curve, Indiana Univ. Math. J. 40 (1991), 333-343.
6. Y. V. EGOROV & M. A. SHUBIN (Editors), Partial Differential Equations, in the series Encyclopedia of Mathematical Sciences, Vol. 30, Springer Verlag 1992, Berlin.
7. N. KAPOULEAS, Compact constant mean curvature surfaces in Euclidean 3-space, J. Diff. Geom. 33 (1991), 683-715.
8. N. KOREVAAR, R. KUSNER, & B. SOLOMON, The structure of complete embedded surfaces with constant mean curvature, J. Diff. Geom. 30 (1989), 465-503.
9. F. LOPEZ & A. ROS, Embedded complete minimal surfaces of genus zero, J. Diff. Geom. 33 (1991), 293-300.
10. R. LÓPEZ & S. MONTIEL, Constant mean curvature surfaces with planar boundary, Duke Math. J. 85 (1996), 583-604.
11. C. MORREY, Multiple Integrals in the Calculus of Variations, Grundlehren Series Volume 130, Springer-Verlag, Berlin, (1966).
12. JOHANNES C.C. NITSCHE, Stationary partitioning of convex bodies, Arch. Rational Mech. and Anal. 89 (1985), 1-19.
13. JOHANNES C.C. NITSCHE, Boundary value problems for variational integrals involving surface curvatures, Quaterly of Applied Mathematics, Vol. LI, No. 2 (1993), 363-387.
14. JOHANNES C.C. NITSCHE, Periodic surfaces that are extremal for energy functionals containing curvature functions. In: Statistical theromodynamics and differential geometry of microstructured materials (Minneapolis, MN, 1991) 69-98, IMA Vol. Math. Appl. 51, Springer, New York, 1993.
15. JOHANNES C.C. NITSCHE, Periodic surfaces that are extremal for energy functionals containing curvature functions. In: Statistical theromodynamics and differential geometry of microstructured materials (Minneapolis, MN, 1991) 69-98, IMA Vol. Math. Appl. 51, Springer, New York, 1993.
16. B. PALMER, The conformal Gauss map and the stability of Willmore surfaces, Ann. Global Analysis Geom. 9 (1991), 305-317.
17. S. D. POISSON, Mémoire sur les surfaces élastiques, Cl. Sci. Mathém. Phys. Inst. de France (1833) 223-331.
18. S. SMALE, On the Morse Index Theorem, J. Math. Mech. 14 (1965), 1049-1055.
19. G. THOMSEN, Über konforme Geometrie I: Grundlagen der konformen Flächentheorie. Abh. Math. Sem. Univ. Hamburg (1923), 31-56.
20. H. WENTE, The symmetry of sessile and pendent drops, Pac. J. Math. 88 (1980), 387-397