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UID:news455@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20181227T174629
DTSTART;TZID=Europe/Zurich:20151202T141500
SUMMARY:Seminar Analysis: Alessandro Carlotto (ETH-ITS Zürich)
DESCRIPTION:Given a closed\,  Riemannian 3-manifold (N\, g) without symmetr
 ies (more precisely:   generic)  and  a  non-negative  integer p\,  can  w
 e  say  something  about  the number of minimal surfaces it contains whose
  Morse index is bounded by p?  More realistically\, can we prove that such
  number is necessarily finite?  This is the classical ”generic finitenes
 s” problem\, which has a rich history and exhibits interesting subtletie
 s even in its basic counterpart concerning closed geodesics on surfaces.  
 We settle such question when g is a bumpy metric of positive scalar curvat
 ure by proving that either finiteness holds or N does contain a copy of RP
 3 in its prime decomposition and we discuss the obstructions to any furthe
 r generalisation of such result. When g is assumed to be strongly bumpy (m
 eaning that all closed\, immersed minimal surfaces do not have Jacobi fiel
 ds\, a notion recently proved to be generic by White) then the finiteness 
 conclusion is true for any compact 3-manifold without boundary.
X-ALT-DESC: \nGiven a closed\,  Riemannian 3-manifold (N\, g) without symme
 tries (more precisely:   generic)  and  a  non-negative  integer p\,  can 
  we  say  something  about  the number of minimal surfaces it contains who
 se Morse index is bounded by p?  More realistically\, can we prove that su
 ch number is necessarily finite?  This is the classical ”generic finiten
 ess” problem\, which has a rich history and exhibits interesting subtlet
 ies even in its basic counterpart concerning closed geodesics on surfaces.
   We settle such question when g is a bumpy metric of positive scalar curv
 ature by proving that either finiteness holds or N does contain a copy of 
 RP<sup>3</sup> in its prime decomposition and we discuss the obstructions 
 to any further generalisation of such result. When g is assumed to be stro
 ngly bumpy (meaning that all closed\, immersed minimal surfaces do not hav
 e Jacobi fields\, a notion recently proved to be generic by White) then th
 e finiteness conclusion is true for any compact 3-manifold without boundar
 y.
DTEND;TZID=Europe/Zurich:20151202T151500
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