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A capillary surface with no radial limits
Mitchell, Colm Patric
Mitchell, Colm Patric
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2017-05
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Dissertation
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Abstract
We begin by discussing the circumstances of capillary surfaces in regions with a corner, both
concave and convex. These circumstances led to the (since proved) Concus-Finn Conjecture,
which gives the requirements for a continuous solution to the capillary problem. We include
the requirements for the existence of radial limits and fans of radial limits in these corner
regions. We outline the method for which conformal mapping of the Gauss map of these
surfaces can be computed to allow the analytic extension of many related theorems. Finally,
we introduce a broadening of the existing research by taking an example done with Dirichlet
conditions in 1996 by Kirk Lancaster and David Siegel and recreating the example with
contact angle data instead.
With the use of contact angle data we find that where in the
original example γ could not be bounded away from zero or π, we were able to find a capillary
surface such that γ is bounded away from 0 and π.
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Thesis (Ph.D.)-- Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics
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Wichita State University
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Copyright 2017 by Colm Patric Mitchell
All Rights Reserved