Open Access Research

Higher genus capillary surfaces in the unit ball of R3

Filippo Morabito

Author Affiliations

Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon, South Korea

School of Mathematics, Korea Institute for Advanced Study, 87 Hoegi-ro, Cheongryangry 2-dong, Seoul, South Korea

Boundary Value Problems 2014, 2014:130  doi:10.1186/1687-2770-2014-130

Published: 22 May 2014

Abstract

We construct the first examples of capillary surfaces of positive genus, embedded in the unit ball of <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/130/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/130/mathml/M2">View MathML</a> with vanishing mean curvature and locally constant contact angles along their three boundary curves. These surfaces come in families depending on one parameter and they converge to the triple equatorial disk. Such surfaces are obtained by deforming the Costa-Hoffman-Meeks minimal surfaces.

MSC: 53A10, 35R35, 53C21.

Keywords:
minimal surface; perturbation method; nonlinear pde’s