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SUMMARY:Green's function estimates and the Poisson equation.  - Ovidiu Mun
 teanu\, University of Connecticut
DTSTART:20191118T150000Z
DTEND:20191118T160000Z
UID:TALK133813@talks.cam.ac.uk
CONTACT:Jessica Guerand
DESCRIPTION:The Green's function of the Laplace operator has been widely s
 tudied in geometric analysis. Manifolds admitting a positive Green's funct
 ion are called nonparabolic. By Li and Yau\, sharp pointwise decay estimat
 es are known for the Green's function on nonparabolic manifolds that have 
 nonnegative Ricci curvature. The situation is more delicate when curvature
  is not nonnegative everywhere. While pointwise decay estimates are genera
 lly not possible in this case\, we have obtained sharp integral estimates 
 for the Green's function on manifolds admitting a Poincare inequality and 
 an appropriate (negative) lower bound on Ricci curvature. This has applica
 tions to solving the Poisson equation\, and to the study of the structure 
 at infinity of such manifolds. 
LOCATION:CMS\, MR13
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