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Local minima of the Gauss curvature of a minimal surface

Published online by Cambridge University Press:  17 April 2009

Shinji Yamashita
Shinji Yamashita
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Minami Osawa, Hachioji Tokyo 192-03, Japan
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Abstract

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Let D be a domain in the complex ω-plane and let x: D → R3 be a regular minimal surface. Let M(K) be the set of points ω0 ∈ D where the Gauss curvature K attains local minima: K(ω0) ≤ K(ω) for |ω – ω0| < δ(ω0), δ(ω0) < 0. The components of M(K) are of three types: isolated points; simple analytic arcs terminating nowhere in D; analytic Jordan curves in D. Components of the third type are related to the Gauss map.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 44 , Issue 3 , December 1991 , pp. 397 - 404
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Nitsche, J.C.C., Vorlesungen über Mintmalflächen (Springer-Verlag, Berlin, Heidelberg, New York, 1975).CrossRefGoogle Scholar
[2]Osserman, R., A survey of minimal surfaces (Van Nostrand Reinhold Company, New York, 1969).Google Scholar
[3]Ruscheweyh, S. and Wirths, K.-J., ‘On extreme Bloch functions with prescribed critical points’, Math. Z. 180 (1982), 91–105.CrossRefGoogle Scholar
[4]Ruscheweyh, S. and Wirths, K.-J., ‘Extreme Bloch functions with many critical points’, Analysis 4 (1984), 237–247.CrossRefGoogle Scholar