A property of complete minimal surfaces

Authors:
Thomas Hasanis and Dimitri Koutroufiotis

Journal:
Trans. Amer. Math. Soc. **281** (1984), 833-843

MSC:
Primary 53C42; Secondary 53A10

DOI:
https://doi.org/10.1090/S0002-9947-1984-0722778-5

MathSciNet review:
722778

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Abstract | References | Similar Articles | Additional Information

Abstract: If is a complete minimal surface in , we denote by the set of points in that do not lie on any tangent plane of . By taking a point in as origin, the position vector of determines a global unit normal vector field to . We prove that if is a minimal section, then is a plane. In particular, the set of tangent planes of a nonflat complete minimal surface in covers all . We also prove a similar result for a complete minimal surface in , and deduce from it that if the spherical image of lies in a closed hemisphere, then is a great .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1984-0722778-5

Keywords:
Minimal surface,
tangent plane,
minimal section,
support function

Article copyright:
© Copyright 1984
American Mathematical Society