Vol. 281, No. 2, 2016

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On the existence of central fans of capillary surfaces

Ammar Khanfer

Vol. 281 (2016), No. 2, 467–479
Abstract

We prove that under some conditions every nonparametric capillary surface which has a central fan (of radial limits at a point O) can be perturbed with respect to the contact angle and the perturbed surfaces continue to have central fans. In particular, any nonparametric capillary surface which is symmetric with respect to a vertical plane through O and has a central fan may be perturbed (with respect to the contact angle) in a nonsymmetric manner and the resulting capillary surfaces will not be symmetric with respect to the vertical plane but will continue to have central fans.

Keywords
capillary surfaces, nonconvex corner, central fans
Mathematical Subject Classification 2010
Primary: 35J93, 76B45
Secondary: 35J62, 53A10
Milestones
Received: 30 August 2013
Revised: 11 August 2015
Accepted: 14 August 2015
Published: 16 February 2016
Authors
Ammar Khanfer
Department of Mathematics and Statistics
Al-Imam Mohammad Ibn Saud Islamic University
P.O. Box 90950
Al-Riyadh 11623
Saudi Arabia