Abstract

We give suficient conditions for the existence of minimal capillary graphs over quadrilaterals symmetric with respect to a diagonal. The proof is constructive, making use of the Weierstrass representation theorem for minimal surfaces. In the process, we construct minimal solutions to the local capillary wedge problem for any wedge angle 0 < φ < π and contact angles γ₁,γ₂ ∈ (0,π) such that |γ₁ −γ₂|≤ π −φ. When |γ₁ −γ₂| < π −φ, the solution presented here has a jump discontinuity at the wedge corner.

Keywords

capillary graph, contact angle, minimal surface, Weierstrass representation, quadrilateral

Mathematical Subject Classification

Primary: 76B45

Secondary: 53A10

Authors