Abstract
We consider simply connected minimal surfaces in Euclidean space and we give a characterisation of the helicoid.
Similar content being viewed by others
References
Jorge, L. and Xavier, F.: A complete minimal surface in R 3 between two parallel planes, Ann. of Math. 112 (1980), 203–206.
McMillan, J. E.: Boundary behaviour of a conformal mapping, Acta Math. 123 (1969), 43–67.
Meeks III, W. H. and Rosenberg, H.: The geometry of periodic minimal surfaces, Comment. Math. Helv. 68 (1993), 538–578.
Plessner, A. I.: Ñber das Verhalten analytischer Funktionen am Rande ihres Definitionsbereichs, J. reine angew. Math. 158 (1927), 219–227.
Pommerenke, Ch.: Boundary Behaviour of Conformal Maps, Springer-Verlag, Berlin, 1992.
Privalov, I. I.: Randeigenschaften analytischer Funktionen, Deutscher Verlag Wiss., Berlin, 1956.
Rodriguez, L. and Rosenberg, H.: Some remarks on complete simply connected minimal surfaces meeting the planes x 3 = constant transversally, J. Geom. Anal., to appear.
Rosenberg, H.: Minimal surfaces of finite type, Bull. Soc. Math. France 123 (1995), 351–359.
Spencer: A function-theoretic identity, Amer. J. Math. 65 (1943), 147–160.
Xavier, F.: Why no new complete simply-connected embedded minimal surfaces have been found since 1776, Preprint.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rosenberg, H., Toubiana, E. Simply Connected Minimal Surfaces in R3 Transverse to Horizontal Planes. Annals of Global Analysis and Geometry 16, 89–100 (1998). https://doi.org/10.1023/A:1006549929232
Issue Date:
DOI: https://doi.org/10.1023/A:1006549929232