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BEGIN:VEVENT
UID:c381e557bf9c98b1505e903b1c3c4c7b
CATEGORIES:Nonlinear Analysis
CREATED:20250325T152646
SUMMARY:Yuxin Ge:  Asymptotically hyperbolic Einstein manifolds in dimension 4
LOCATION:Hill 705
DESCRIPTION:Abstract: Given a closed riemannian manfiold of dimension 3 $(M^3, [h])$, w
 hen will we fill in an asymptotically hyperbolic Einstein manifold of dimen
 sion 4 $(X^4, g_+)$ such that $r^2 g_+|_M= h$ on the boundary $M=partial X$
  for some defining function $r$ on $X^4$? This problem is motivated by the 
 correspondance AdS/CFT in quantum gravity proposed by Maldacena in 1998 et 
 comes also from the study of the structure of asymptotically hyperbolic Ein
 stein manifolds. In this talk, I discuss the compactness issue of asymptoti
 cally hyperbolic Einstein manifolds in dimension 4, that is, how the compac
 tness on conformal infinity leads to the compactness of the compactificatio
 n of such manifolds under the suitable conditions on the topology and on so
 me conformal invariants. As application, I discuss some recent progress on 
 the existence result.\n
X-ALT-DESC;FMTTYPE=text/html:<p style="color: #000000; font-family: -webkit-standard; font-weight: 400; 
 letter-spacing: normal; text-align: left; text-indent: 0px; text-transform:
  none; white-space: normal; word-spacing: 0px; text-decoration: none;"><str
 ong>Abstract:&nbsp;</strong>Given a closed riemannian manfiold of dimension
  3 $(M^3, [h])$, when will we fill in an asymptotically hyperbolic Einstein
  manifold of dimension 4 $(X^4, g_+)$ such that $r^2 g_+|_M= h$ on the boun
 dary $M=partial X$ for some defining function $r$ on $X^4$? This problem is
  motivated by the correspondance AdS/CFT in quantum gravity proposed by Mal
 dacena in 1998 et comes also from the study of the structure of asymptotica
 lly hyperbolic Einstein manifolds. In this talk, I discuss the compactness 
 issue of asymptotically hyperbolic Einstein manifolds in dimension 4, that 
 is, how the compactness on conformal infinity leads to the compactness of t
 he compactification of such manifolds under the suitable conditions on the 
 topology and on some conformal invariants. As application, I discuss some r
 ecent progress on the existence result.</p>
CONTACT:Rutgers University
DTSTAMP:20260927T051840
DTSTART;TZID=America/New_York:20250408T134000
DTEND;TZID=America/New_York:20250408T144000
SEQUENCE:0
TRANSP:OPAQUE
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