Higher genus capillary surfaces in the unit ball of
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:10.1186/1687-2770-2014-130Published: 22 May 2014
We construct the first examples of capillary surfaces of positive genus, embedded in the unit ball of 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.