\noindent{\bf Mathematisches Oberseminar} {\it PDG und
Spektraltheorie} (WiSe 2013/14).

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\noindent{\bf Date:} 16.01.2014.

\noindent{\bf Time and place:} 14:15 in B 134.

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\noindent{\bf Speaker:} Anna Dall'Acqua (Universit{\"a}t Ulm).

\noindent{\bf Titel:} {\it Unstable Willmore surfaces}. 


\noindent{\bf Abstract:}

\noindent In the class of surfaces with fixed boundary, critical points of the Willmore
functional are naturally found to be those solutions of the Euler-Lagrange equation where
the mean curvature on the boundary vanishes. We consider the case of symmetric surfaces
of revolution in the setting where there are two families of stable solutions given by the
catenoids. In this talk we discuss a existence result on a third family of solutions which
are unstable critical points of the Willmore functional, and which spatially lie between the
upper and lower families of catenoids. Our method does not require any kind of smallness
assumption, and allows us to derive some additional interesting qualitative properties of the
solutions.



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Thomas {\O}stergaard S{\o}rensen

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