Quaternionic holomorphic geometry: Plücker formula, Dirac eigenvalue estimates and energy estimates of harmonic 2-tori

Inventiones Mathematicae

Volumn 146, Issue 3, 2001, Pages 507-593

  Ferus, D ^a   Leschke, K ^a   Pedit, F ^b   Pinkall, U ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035622710     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220100173     Document Type: Article

References (26)

1. N. Aronszajn. A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order. J. Math. Pur. Appl. 36 (1957), 235-249
2. C. Bär. Lower eigenvalue estimates for Dirac operators. Math. Ann. 293 (1992), 39-46
3. W. Blaschke. Vorlesungen über Differentialgeometrie III, Differentialgeometrie der Kreise und Kugeln. Grundlehren 29, Springer, Berlin 1929
4. A. Bobenko. Surfaces of constant mean curvature and integrable equations. Russian Math. Surveys 46 (1991), 1-45
5. C. Bohle, P. Peters. Soliton spheres. In preparation
6. R. Bryant. A duality theorem for Willmore surfaces. J. Differential Geom. 20 (1984), 23-53
7. 4 and quaternions. Sfb288 Preprint 441 and http://arXiv.org/abs/math/0002075
8. H. Choi, A. Wang. A first eigenvalue estimate for minimal hypersurfaces. J. Diff. Geom. 18 (1983), 559-562
9. J. Eells, J.C. Wood. Restrictions on harmonic maps of surfaces. Topology 15 (1976), 263-266
10. N(1). Proc. Lond. Math. Soc., III Ser. 57 (1988), No. 2, 383-416
11. A.M. Garcia. On the conformal types of algebraic surfaces in euclidean space. Comment. Math. Helv. 37 (1962), 49-60
12. P. Griffiths, J. Harris. Principles of algebraic geometry. John Wiley & Sons, Inc., New York, 1994
13. P. Hartman, A. Wintner. On the local behavior of solutions of non-linear parabolic differential equations. Amer. J. Math. 75 (1953), 449-476
14. M. Heil. Numerical tools for the study of finite gap solutions of integrable systems. Thesis, TU-Berlin, 1995
15. N. Hitchin. Harmonic maps from a 2-torus to the 3-sphere. J. Diff. Geom. 31 (1990), 627-710
16. H.B. Lawson, M.L. Michelson. Spin Geometry. Princeton University Press
17. K. Leschke. Willmore bundles. In preparation
18. S. Montiel. Willmore two-spheres in the four-sphere. Trans. Amer. Math. Soc. 352 (2000), 4469-4486
19. R. Palais. Seminar on the Atiyah-Singer index theorem. Princeton University Press, 1965
20. F. Pedit, U. Pinkall. Quaternionic analysis on Riemann surfaces and differential geometry. Doc. Math. J. DMV, Extra Volume ICM 1998, Vol. II, 389-400
21. J. Richter. Conformal surface theory via Quaternions. Thesis, TU-Berlin, 1996
22. Y. Rodin. Generalized analytic functions on Riemann surfaces. LNM 1288, Springer Verlag, Berlin
23. E.A. Ruh, J. Vilms. The tension field of the Gauss map. Trans. Amer. Math. Soc. 149 (1970), 569-573
24. M. Schmidt. Private communication
25. 3, the Willmore numbers, and soliton spheres. Proc. Steklov Inst. Math. 225 (1999), 322-343
26. 3. Actas II Coloq. Int. Geom. Differencial, Santiago Compostela, 1967, 7-9 (1968)