Remarks on the behavior of nonparametric capillary surfaces at corners
Lancaster, Kirk E.
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Lancaster, Kirk E. 2012. Remarks on the behavior of nonparametric capillary surfaces at corners. Pacific Journal of Mathematics, v.258 no.2 pp.369-392
Consider a nonparametric capillary or prescribed mean curvature surface z = f(x) defined in a cylinder Omega x R over a two-dimensional region Omega whose boundary has a corner at O with an opening angle of 2 alpha. Suppose the contact angle approaches limiting values gamma(1) and gamma(2) in (0, pi) 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 (gamma(1), gamma(1)) is an element of D-1(+/-) boolean OR D-2(+/-) and discuss the continuity of the Gauss map.
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