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Miyuki Koiso （Kyushu Univ. IMI） |
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| Title : Free boundary problem for surfaces with constant mean curvature |
Abstract
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We study embedded surfaces of constant mean curvature with free boundary
in given supporting planes in the euclidean three-space. We assume that
each considered surface meets the supporting planes with constant
contact angle. These surfaces are characterized as equilibrium surfaces
of the variational problem of which the total energy is the surface area
and a wetting energy (that is a weighted area of the domains in the
supporting planes bounded by the boundary of the considered surface)
with volume constraint. An equilibrium surface is said to be stable if
the second variation of the energy is nonnegative for all volume-
preserving variations satisfying the boundary condition. We are
interested in determining all (stable) solutions. At present in
literature, only for some special cases, for example, the supporting
planes are either just a single plane or two parallel planes and the
wetting energy is nonnegative, all stable solutions are known. We
discuss recent progress of this subject and show the space of solutions
is not continuous with respect to the boundary condition.
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Organizer: Reiko Miyaoka
Contact：
Grants-in-Aids for Scientific research：23340012 |
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