zbMATH — the first resource for mathematics

Construction de surfaces minimales en recollant des surfaces de Scherk. (Minimal surfaces constructed by gluing Scherk surfaces.). (French) Zbl 0860.53004
Summary: We construct simply periodic minimal surfaces in Euclidean 3-space by gluing together Scherk surfaces, using the techniques of N. Kapouleas.

53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
Full Text: DOI Numdam EuDML
[1] T. AUBIN, Non linear analysis on manifolds, Monge Ampere Equations, Springer Verlag, 1982. · Zbl 0512.53044
[2] M.P. DO CARMO, Riemannian geometry, Birkhäuser, 1992.
[3] S. GALLOT, D. HULIN, J. LAFONTAINE, Riemannian geometry, second edition, Springer Verlag, 1990. · Zbl 0716.53001
[4] D. GILBARG and N.S. TRUDINGER, Elliptic partial differential equations of second order, 2nd Edition, Springer Verlag, 1983. · Zbl 0562.35001
[5] N. KAPOULEAS, Complete constant mean curvature surfaces in Euclidean three-space, Annals of Math., 131 (1990), 239-330. · Zbl 0699.53007
[6] H. KARCHER, Embedded minimal surfaces derived from Scherk’s examples, Manuscripta Math., 62 (1988), 83-114. · Zbl 0658.53006
[7] H. KARCHER, Construction of minimal surfaces, Surveys in Geometry, University of Tokyo (1989), 1-96, et Lecture Notes n° 12, SFB256, Bonn (1989).
[8] H. KARCHER, The triply periodic surfaces of alan schoen and their constant mean curvature companions, Manuscripta Math., 64 (1989), 291-357. · Zbl 0687.53010
[9] H. KARCHER, Construction of higher genus embedded minimal surfaces, Geom. and Top. of Submanifolds III World Sc. (1990), 174-191. · Zbl 0737.53007
[10] W.H. MEEKS, H. ROSENBERG, The geometry of periodic minimal surfaces, Comment. Math. Helvetici, 68 (1993), 538-578. · Zbl 0807.53049
[11] H. ROSENBERG, Some recent developments in the theory of properly embedded minimal surfaces in ℝ3, Séminaire Bourbaki, n° 759 (1992). · Zbl 0789.53003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.