Remarks on the behavior of nonparametric capillary surfaces at corners
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
Click on the DOI link to access the article (may not be free).