Vol. 258, No. 2, 2012

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Remarks on the behavior of nonparametric capillary surfaces at corners

Kirk E. Lancaster

Vol. 258 (2012), No. 2, 369–392

Consider a nonparametric capillary or prescribed mean curvature surface z = f(x) defined in a cylinder Ω × over a two-dimensional region Ω whose boundary has a corner at 𝒪 with an opening angle of 2α. Suppose the contact angle approaches limiting values γ1 and γ2 in (0) as 𝒪 is approached along each side of the opening angle. We will prove the nonconvex Concus–Finn conjecture, determine the exact sizes of the radial limit fans of f at 𝒪 when (γ11) D1±D2± and discuss the continuity of the Gauss map.

capillary graph, Concus–Finn conjecture, Gauss map, sizes of fans
Mathematical Subject Classification 2010
Primary: 76B45, 35J93
Secondary: 53A10, 35J62
Received: 12 July 2010
Revised: 8 July 2012
Accepted: 21 July 2012
Published: 1 August 2012
Kirk E. Lancaster
Department of Mathematics and Statistics
Wichita State University
Wichita, KS 67260-0033
United States