Abstract

This paper follows previous work by Huff and McCuan, who provided for 0 < γ < π a geometric construction of minimal capillary graphs over a square with constant contact angles on the edges alternating between γ and π − γ. Here the result is extended to regular 2n-gons. Regularity results are obtained for these graphs, and explicit, conformal parametrizations are given for the Jenkins–Serrin graphs corresponding to γ ∈{0,π}.

Keywords

capillarity, contact angle, minimal surface, Weierstrass representation

Mathematical Subject Classification

Primary: 76B45

Secondary: 53A10

Authors