Proceedings of the American Mathematical Society

Author(s): Yi Fang; Fusheng Wei
Journal: Proc. Amer. Math. Soc. 126 (1998), 1531-1539.
MSC (1991): Primary 53A10; Secondary 35P99
Retrieve article in: PDF
This article is available free of charge

Abstract: We prove that a properly embedded minimal annulus with one flat end, bounded in a slab by lines or circles, is a part of a Riemann's example.

1.: L. Barbosa and M. do Carmo. On the size of a stable minimal surface in $\mathbb{R}^{3}$ . Amer. J. of Math., 98:515-28, 1976. MR 54:1292
2.: M. Callahan, D. Hoffman and W. Meeks III. The structure of singly-periodic minimal surfaces. Invent. math., 99:455-81, 1990. MR 92a:53005
3.: I. Chavel. Eigenvalues in Riemannian Geometry. Academic Press, Inc. Orlando, San Diego, New York, London, Montreal, Sydney, Tokyo, 1984. MR 86g:58140
4.: U. Dierkes, S. Hildebrandt, A. Küster and O. Wohlrab. Minimal Surfaces I, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, Hong Kong, Barcelona, Budapest, 1992. MR 94c:49001a
5.: Y. Fang. On minimal annuli in a slab. Comment. Math. Helvetici, 69:417-30, 1994. MR 95f:53014
6.: Y. Fang. Total curvature of branched minimal surfaces. Proc. Amer. Math. Soc., 124(6):1895-98, 1996. MR 96h:53011
7.: D. Hoffman, H. Karcher, and H. Rosenberg. Embedded minimal annuli in $\mathbb{R}^{3}$ bounded by a pair of straight lines. Comment. Math. Helvetici, 66:599-617, 1991. MR 93d:53012
8.: D. Hoffman and W. Meeks III. The asymptotic behavior of properly embedded minimal surfaces of finite topology. J. of Amer. Math. Soc., 2(4):667-682, 1989. MR 90f:53010
9.: S. B. Jackson. Vertices for plane curves. Bull. of Amer. Math. Soc. 50:564-78, 1944. MR 6:100e
10.: F. López, M. Ritoré and F. Wei. A characterization of Riemann's minimal surfaces. to appear in Journal of Differential Geometry.
11.: W. Meeks. The geometry, topology, and existence of periodic minimal surfaces Proceedings of Symposia in Pure Mathematics 54:333-373, 1993. MR 94k:53013
12.: J. C. C. Nitsche. Lectures on Minimal Surfaces, Vol. I. Cambridge University Press, Cambridge, New York, New Rochelle, Melbourne, Sydney, 1989. MR 90m:49031
13.: R. Osserman. A Survey of Minimal Surfaces. Dover, Publications, Inc. New York, 1986. MR 87j:53012
14.: J. Pérez and A. Ros Some uniqueness and nonexistence theorems for embedded minimal surfaces. Math. Ann. 295:513-525, 1993. MR 94a:53020
15.: P. Romon. A rigidity theorem for Riemann's minimal surfaces. Ann. Inst. Fourier, Grenoble, 43(2):485-502, 1993. MR 94c:53010
16.: M. Shiffman. On surfaces of stationary area bounded by two circles, or convex curves, in parallel planes. Annals of Math. 63:77-90, 1956. MR 17:632d
17.: E. Toubiana. On the minimal surfaces of Riemann. Comment. Math. Helvetici 67:546-70, 1992. MR 93i:53010

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 53A10, 35P99

Yi Fang
Affiliation: Centre for Mathematics and its Applications School of Mathematical Sciences Australian National University Canberra, ACT 0200, Australia
Email: yi@maths.anu.edu.au

Fusheng Wei
Affiliation: Department of Mathematics, Virginia Polytechnic Institute and State University Blacksburg, Virginia 24061-0123
Email: fwei@calvin.math.vt.edu

DOI: 10.1090/S0002-9939-98-04441-4
PII: S 0002-9939(98)04441-4
Received by editor(s): October 21, 1996
Additional Notes: The first author is supported by the Australian Research Council.
Communicated by: Peter Li
Copyright of article: Copyright 1998, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS