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UID:news487@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20181229T175840
DTSTART;TZID=Europe/Zurich:20130925T151500
SUMMARY:Seminar Analysis: Andrea Mondino (ETH Zurich)
DESCRIPTION: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 s
 econd  fundamental form. Minimizers\, and more generally critical points o
 f such  functionals can be seen respectively as GENERALIZED minimal\, tota
 lly  geodesic and totally umbilical immersions. In the seminar I will revi
 ew  some results (obtained in collaboration with Kuwert\, Rivière and  Sh
 ygulla) regarding the existence and the regularity of minimizers of  such 
 functionals. An interesting observation regarding the results  obtained wi
 th Rivière is that the theory of Willmore surfaces can be  usesfull to co
 mplete the theory of minimal surfaces (in particular in  relation to the e
 xistence of canonical smooth representatives in  homotopy classes\, a clas
 sical program started by Sacks and Uhlenbeck).
X-ALT-DESC: \nGiven 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 mea
 n 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\, to
 tally  geodesic and totally umbilical immersions. In the seminar I will re
 view  some results (obtained in collaboration with Kuwert\, Rivière and  
 Shygulla) regarding the existence and the regularity of minimizers of  suc
 h functionals. An interesting observation regarding the results  obtained 
 with Rivière is that the theory of Willmore surfaces can be  usesfull to 
 complete the theory of minimal surfaces (in particular in  relation to the
  existence of canonical smooth representatives in  homotopy classes\, a cl
 assical program started by Sacks and Uhlenbeck).
DTEND;TZID=Europe/Zurich:20130925T161500
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