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SUMMARY:Amir Moradifam (University of California\, Riverside)
DTSTART:20250918T150000Z
DTEND:20250918T160000Z
DTSTAMP:20260423T040150Z
UID:GARF/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GARF/5/">The
  Sphere Covering Inequality and Its Applications</a>\nby Amir Moradifam (U
 niversity of California\, Riverside) as part of Geometric Analysis and Rel
 ated Fields\n\n\nAbstract\nWe show that the total area of two distinct Gau
 ssian curvature 1 surfaces with the same conformal factor on the boundary\
 , which are also conformal to the Euclidean unit disk\, must be at least 4
 π. In other words\, the areas of these surfaces must cover the whole unit
  sphere after a proper rearrangement. We refer to this lower bound of tota
 l areas as the Sphere Covering Inequality. This inequality and its general
 izations are applied to a number of open problems related to Moser-Truding
 er type inequalities\, mean field equations and Onsager vortices\, etc\, a
 nd yield optimal results. In particular we confirm the best constant of a 
 Moser-Truidinger type inequality conjectured by A. Chang and P. Yang in 19
 87. This is a joint work Changfeng Gui.\n\nGoogle meet room: https://meet.
 google.com/wha-yopd-trc\n
LOCATION:https://researchseminars.org/talk/GARF/5/
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