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SUMMARY:Antoine Song (California Institute of Technology)
DTSTART:20221123T130000Z
DTEND:20221123T150000Z
DTSTAMP:20260423T040041Z
UID:NCTS-GMT/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NCTS-GMT/13/
 ">The spherical Plateau problem: existence\, uniqueness\, stability</a>\nb
 y Antoine Song (California Institute of Technology) as part of NCTS intern
 ational Geometric Measure Theory seminar\n\n\nAbstract\nConsider a countab
 le group $G$ acting on the unit sphere $S$ in the\nspace of $L^2$ function
 s on $G$ by the regular representation. Given a\nhomology class $h$ in the
  quotient space $S/G$\, one defines the\nspherical Plateau solutions for $
 h$ as the intrinsic flat limits of\nvolume minimizing sequences of cycles 
 representing $h$. Interestingly in\nsome special cases\, for example when 
 $G$ is the fundamental group of a\nclosed hyperbolic manifold of dimension
  at least $3$\, the spherical\nPlateau solutions are essentially unique an
 d can be identified. However\nin general not much is known. I will discuss
  the questions of existence\nand structure of non-trivial Plateau solution
 s. I will also explain how\nuniqueness of spherical Plateau solutions for 
 hyperbolic manifolds of\ndimension at least $3$ implies stability for the 
 volume entropy\ninequality of Besson-Courtois-Gallot.\n
LOCATION:https://researchseminars.org/talk/NCTS-GMT/13/
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