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Carissimi,<br>
<br>
vi segnalo il prossimo seminario di ED a Tor Vergata:<br>
<br>
<b>Martedi' 14 Gennaio 2014, h 14:15, Aula Dal Passo</b><b><br>
</b><b>Andrea Mondino (ETH Zurich)</b><b><br>
</b><b>"Willmore spheres in Riemannian manifolds" </b><b><br>
</b><b>Given an immersion f of the 2-sphere in a Riemannian manifold
(M,g) we study quadratic curvature functionals of the type:
\int_{f(S^2)} H^2, \int_f(S^2) A^2, \int_{f(S^2)} )|Aº|^2, where H
is the mean curvature, A is the second fundamental form, and Aº is
the tracefree second fundamental form. Minimizers, and more
generally critical points of such functionals can be seen
respectively as GENERALIZED minimal, totally geodesic and totally
umbilical immersions. In the seminar I will review some results
(obtained in collaboration with Kuwert, Rivière and Shygulla)
regarding the existence and the regularity of minimizers of such
functionals. An interesting observation regarding the results
obtained with Rivière is that the theory of Willmore surfaces can
be usesful to complete the theory of minimal surfaces (in
particular in relation to the existence of canonical smooth
representatives in homotopy classes, a classical program started
by Sacks and Uhlenbeck).</b><br>
<br>
<pre class="moz-signature" cols="72">--
Daniele Castorina
Dipartimento di Matematica - Studio 1221
Università di Roma "Tor Vergata"
Via della Ricerca Scientifica 00133 Roma
email: <a class="moz-txt-link-abbreviated" href="mailto:castorin@mat.uniroma2.it">castorin@mat.uniroma2.it</a>
tel: +390672594653</pre>
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