Some structure theorems for complete constant mean curvature surfaces with boundary a convex curve
Authors:
Ricardo Sa Earp and Harold Rosenberg
Journal:
Proc. Amer. Math. Soc. 113 (1991), 1045-1053
MSC:
Primary 53A10; Secondary 49Q05, 53C45
DOI:
https://doi.org/10.1090/S0002-9939-1991-1072337-1
MathSciNet review:
1072337
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be a properly embedded, connected, complete surface in
with non-zero constant mean curvature and with boundary a strictly convex plane curve
. It is shown that if
is contained in a vertical cylinder of
, outside of some compact set of
, and if
is contained in a half-space of
determined by
, then
inherits the symmetries of
. In particular,
is a Delaunay surface if
is a circle. It is also shown that if
has a finite number of vertical annular ends and the area of the flat disc
bounded by
is not "too small," then
lies in a half-space.
- [1] F. Brito, R. Earp, W. Meeks, and H. Rosenberg, Structure theorems for constant mean curvature surfaces bounded by a planar curve, Indiana Math. J. 40 (1991), 333-343. MR 1101235 (93e:53009)
- [2] H. Hopf, Lectures on differential geometry in the large. Lecture Notes in Math., vol. 1000, 1983, Springer-Verlag, New York. MR 707850 (85b:53001)
- [3] N. Korevaar, R. Kusner, and B. Solomon, The structure of complete embedded surfaces with constant mean curvature, J. Differential Geom. 30 (1989), pp. 465-503. MR 1010168 (90g:53011)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1991-1072337-1
Keywords:
Constant mean curvature,
Delaunay surface,
Alexandrov reflection principle
Article copyright:
© Copyright 1991
American Mathematical Society