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SUMMARY:Wolfgang Ziller (UPenn)
DTSTART:20210921T140000Z
DTEND:20210921T150000Z
DTSTAMP:20260417T091327Z
UID:CHEM/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CHEM/2/">On 
 the Palais-Smale condition for the prescribed Ricci curvature functional a
 nd the existence of saddle points</a>\nby Wolfgang Ziller (UPenn) as part 
 of Workshop on compact homogeneous Einstein manifolds\n\n\nAbstract\nGiven
  a metric $T$\, we want to solve the\nequation $Ric(g)=cT$ for a metric $g
 $ (and a constant $c$). It is well known that they are critical points of 
 the scalar curvature $Scal$ under the constraint $\\operatorname{tr}_gT=1$
 . We study this problem in the case of homogeneous spaces $G/H$. For the c
 orresponding\nproblem for Einstein metrics it was shown that $Scal$ satisf
 ies the Palais-Smale condition\, which gives rise to a large class of Eins
 tein metrics which are saddle points of the functional. We will discuss th
 is condition in our case and will see that Palais-Smale  is not satisfied\
 , and how one can nevertheless use a mountain pass type argument to produc
 e saddle points. This is joint work with Artem Pulemotov.\n
LOCATION:https://researchseminars.org/talk/CHEM/2/
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