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    Remarks on the behavior of nonparametric capillary surfaces at corners

    Date
    2012-08
    Author
    Lancaster, Kirk E.
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    Citation
    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
    Abstract
    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.
    Description
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    URI
    http://hdl.handle.net/10057/6060
    http://dx.doi.org/10.2140/pjm.2012.258.369
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