Keywords
- Vector Field
- Minimal Surface
- Degree Theory
- Conformal Group
- Index Zero
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References
Alt, H.W.: Verzweigungspunkte von H-Flächen I, Math. Z. 127, 333–362 (1972); II, Math. Ann. 201, 33–56 (1973).
Böhme, R. and Tromba, A.J.: The index theorem for classical minimal surfaces; Annals of Mathematics 113 (1981), pp. 447–499
Elworthy, K.D. and Tromba, A.J.: Differential structures and Fredholm maps on Banach manifolds; Proc. Pure Math. vol. 15, AMS (1970), pp. 45–94.
Elworthy, K.D. and Tromba, A.J.: Degree theory on Banach manifolds; Proc. Symp. Pure Math. Vol 18, AMS (1970), pp. 86–94.
Gulliver, R.: Regularity of minimizing surfaces of prescribed mean curvature; Ann. of Math. 97, 275–305 (1973).
Heinz, E. and Tomi, F.: Zu einem Satz von Hildebrandt über das Randverhalten von Minimalflächen; Math. Z. 111 (1969), 372–386.
Hildebrandt, S.: Boundary behavior of minimal surfaces; Arch. Rational Mech. Anal. 35 (1969), pp. 47–81.
Leray, J. and Schauder, J.: Topologie et equations fonctionelles; Ann. Sci. Ecole Norm. Sup. 51 (1934), pp. 45–78.
Nirenberg, L.: Variational and topological methods in non-linear problems; Bull. AMS 4 (1981), 267–302.
Osserman, R.: A proof of the regularity everywhere of the classical solution of Plateau’s problem; Ann. of Math. (2) 91 (1970), pp. 550–569.
Smale, S.: An infinite dimensional version of Sard’s theorem; Amer. J. Math. 87 (1965), pp. 861–866.
Struwe, M.: On a critical point theory of minimal surfaces spanning a wire in IRn; J. Reine Angew. Math. 349 (1984), pp. 1–23.
Tomi, F. and Tromba, A.J.: On the structure of the set of curves bounding minimal surfaces of prescribed degeneracy; J. Reine Angew. Math. 316 (1980), 31–43.
Thiel, U.: On the stratification of branched minimal surfaces; Analysis 5 (1985), 251–271.
Tromba, A.J.: Degree theory on oriented infinite dimensional varieties and the Morse number spanning a curve in IRn, Part II, n = 3; Manuscripta math. 48 (1984), pp. 139–161; Part I, Trans. AMS, vol. 290, Number 1 (July 1985), pp. 385–413.
Tromba, A.J.: A general asymptotic fixed point theorem; J. Reine Angew. Math. 332 (1982), pp. 118–123.
Tromba, A.J.: On the number of simply connected minimal surfaces spanning a curve; Memoirs of the AMS, 12 194, (1977).
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© 1988 Springer-Verlag
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Tromba, A.J. (1988). Open problems in the degree theory for disc minimal surfaces spanning a curve in ℝ3 . In: Hildebrandt, S., Leis, R. (eds) Partial Differential Equations and Calculus of Variations. Lecture Notes in Mathematics, vol 1357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082876
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DOI: https://doi.org/10.1007/BFb0082876
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