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MAXIMAL ANNULI WITH PARALLEL PLANAR BOUNDARIES IN THE THREE-DIMENSIONAL LORENTZ–MINKOWSKI SPACE

Part of: Global differential geometry Classical differential geometry

Published online by Cambridge University Press:  27 January 2010

JUNCHEOL PYO
JUNCHEOL PYO*
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-742, Korea (email: jcpyo@snu.ac.kr)
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Abstract

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We prove that maximal annuli in 𝕃3 bounded by circles, straight lines or cone points in a pair of parallel spacelike planes are part of either a Lorentzian catenoid or a Lorentzian Riemann’s example. We show that under the same boundary condition, the same conclusion holds even when the maximal annuli have a planar end. Moreover, we extend Shiffman’s convexity result to maximal annuli; but by using Perron’s method we construct a maximal annulus with a planar end where a Shiffman-type result fails.

Keywords

Lorentzian catenoidmaximal annulus surfaceLorentzian Riemann’s example

MSC classification

Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) 53A10: Minimal surfaces, surfaces with prescribed mean curvature
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 2 , April 2010 , pp. 208 - 222
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

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