Existence of minimizing willmore surfaces of prescribed genus

International Mathematics Research Notices

Volumn , Issue 10, 2003, Pages 553-576

  Bauer, Matthias ^a   Kuwert, Ernst ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038374781     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/s1073792803208072     Document Type: Article

References (10)

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3. _, Estimates for the biharmonic energy on unbounded planar domains, and the existence of surfaces of every genus that minimize the squared-mean-curvature integral, Elliptic and Parabolic Methods in Geometry (Minneapolis, Minn, 1994), A K Peters, Massachusetts, 1996, pp. 67-72.
4. 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), no. 2, 269-291.
5. M. U. Schmidt, A proof of the Willmore conjecture, Sfb 288 Preprint No. 546, Berlin, 2002.
6. R. Schoen and S.-T. Yau, Lectures on Differential Geometry, Conference Proceedings and Lecture Notes in Geometry and Topology, vol. I, International Press, Massachusetts, 1994.
7. L. Simon, Existence of Willmore surfaces, Miniconference on Geometry and Partial Differential Equations (Canberra, 1985), Proceedings of the Centre for Mathematical Analysis, Australian National University, vol. 10, Australian National University, Canberra, 1986, pp. 187-216.
8. _, Existence of surfaces minimizing the Willmore functional, Comm. Anal. Geom. 1 (1993), no. 2, 281-326.
9. T. J. Willmore, Note on embedded surfaces, An. Şti. Univ. "Al. I. Cuza" Iaşi Secţ. I a Mat. (N.S.) 11B (1965), 493-496.
10. _, Riemannian Geometry, Oxford Science Publications, Oxford University Press, New York, 1993.