On the number of minimal surfaces with a given boundary

Géométrie différentielle, physique mathématique, mathématiques et société (II) - Volume en l'honneur de Jean-Pierre Bourguignon, Astérisque no. 322 (2008), p. 207-224

MR 2521657 | Zbl 1184.53012

@incollection{AST_2008__322__207_0,
     author = {Hoffman, David and White, Brian},
     title = {On the number of minimal surfaces with a given boundary},
     booktitle = {G\'eom\'etrie diff\'erentielle, physique math\'ematique, math\'ematiques et soci\'et\'e (II) - Volume en l'honneur de Jean-Pierre Bourguignon},
     editor = {Hijazi Oussama},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {322},
     year = {2008},
     pages = {207-224},
     zbl = {1184.53012},
     mrnumber = {2521657},
     language = {en},
     url = {http://www.numdam.org/item/AST_2008__322__207_0}
}

Hoffman, David; White, Brian. On the number of minimal surfaces with a given boundary, in Géométrie différentielle, physique mathématique, mathématiques et société (II) - Volume en l'honneur de Jean-Pierre Bourguignon, Astérisque, no. 322 (2008), pp. 207-224. http://www.numdam.org/item/AST_2008__322__207_0/

References

[1] D. Hoffman & B. White - "Genus-one helicoids from a variational point of view", Comment Math. Helv. 83 (2008), p. 767-813. | MR 2442963 | Zbl 1161.53009

[2] D. Hoffman & B. White, "The geometry of genus-one helicoids", to appear in Comment. Math. Helv. | MR 2507253 | Zbl 1168.53006

[3] D. Hoffman & B. White, "Helicoid-like minimal surfaces of arbitrary genus in $S^{2} \times R$ ", in preparation.

[4] F. Tomi & A. J. Tromba - "Extreme curves bound embedded minimal surfaces of the type of the disc", Math. Z. 158 (1978), p. 137-145. | Article | MR 486522 | Zbl 0353.53032

[5] A. J. Tromba - "Degree theory on oriented infinite-dimensional varieties and the Morse number of minimal surfaces spanning a curve in $𝐑^{n}$ ", Manuscripta Math. 48 (1984), p. 139-161. | Article | MR 753728 | Zbl 0622.58006

[6] B. White - "Curvature estimates and compactness theorems in $3$ -manifolds for surfaces that are stationary for parametric elliptic functionals", Invent. Math. 88 (1987), p. 243-256. | Article | MR 880951 | Zbl 0615.53044

[7] B. White, "The space of $m$ -dimensional surfaces that are stationary for a parametric elliptic functional", Indiana Univ. Math. J. 36 (1987), p. 567-602. | Article | MR 905611 | Zbl 0770.58005

[8] B. White, "New applications of mapping degrees to minimal surface theory", J. Differential Geom. 29 (1989), p. 143-162. | Article | MR 978083 | Zbl 0638.58005

[9] B. White, "Which ambient spaces admit isoperimetric inequalities for submanifolds?", to appear in J. Differential Geometry, 2008. | MR 2545035 | Zbl 1179.53061