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SUMMARY:Stability of the elliptic Harnack Inequality - Martin Barlow (UBC)
DTSTART:20220905T153000Z
DTEND:20220905T163000Z
UID:TALK178463@talks.cam.ac.uk
CONTACT:Jason Miller
DESCRIPTION:A manifold has the Liouville property if every bounded harmoni
 c function is constant. A theorem of T.\\ Lyons is that the Liouville prop
 erty is not preserved under mild perturbations of the space.  Stronger con
 ditions on a space\, which imply the Liouville property\,are the parabolic
  and elliptic Harnack inequalities (PHI and EHI). In the early 1990s Grigo
 r'yan and Saloff-Coste gave a characterisation of the parabolic Harnack in
 equality (PHI)\, which immediately gives its stability under mild perturba
 tions. In this talk we prove  the stability of the EHI. The proof uses the
  concept of a quasi symmetric transformation of a metric space\, and the i
 ntroduction of these ideas to Markov processes suggests a number of new pr
 oblems.  (Based on joint work with Mathav Murugan.)
LOCATION:MR9\, Centre for Mathematical Sciences
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