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Remarks on the
behavior of nonparametric capillary surfaces at corners
Kirk E. Lancaster |
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Vol. 258 (2012), No. 2, 369–392
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Abstract |
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Consider a nonparametric capillary or prescribed mean curvature surface z = f(x) defined in a cylinder Ω × ℝ 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,π) 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 (γ1,γ1) ∈ D1±∪ D2± and discuss the continuity of the Gauss map. |
Keywords
capillary graph, Concus–Finn conjecture, Gauss map, sizes
of fans
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Mathematical Subject Classification 2010
Primary: 76B45, 35J93
Secondary: 53A10, 35J62
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Milestones
Received: 12 July 2010
Revised: 8 July 2012
Accepted: 21 July 2012
Published: 1 August 2012
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Authors |
| Kirk E. Lancaster | |
| Department of Mathematics and
Statistics Wichita State University Wichita, KS 67260-0033 United States |
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