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SUMMARY:Removable sets for pseudoconvexity for weakly smooth boundaries
DTSTART:20251124T130000Z
DTEND:20251124T140000Z
DTSTAMP:20260506T113000Z
UID:indico-event-15247@indico.math.cnrs.fr
DESCRIPTION:Speakers: Pascal Thomas (IMT - Université de Toulouse)\n\nThe
  natural domains of existence of holomorphic functions in several variable
 s are characterized by pseudoconvexity\, which turns out to be a local con
 dition on their boundaries. In the case where said boundary is $\\mathcal 
 C^{2}$-smooth\, this can be understood as a sort of infinitesimalplurisubh
 armonicity along the complex tangential directions\, and written explicitl
 y in terms of the Levi form of the defining function of the domain\, which
  produces a non-linear second order partial differential inequation on the
  defining function.\nWe show that for bounded domains in $\\C^n$ with $\\m
 athcal C^{1\,1}$ smooth boundary\, if there is a closed set $F$ of $2n-1$-
 Lebesgue measure $0$ such that $\\partial \\Om \\setminus F$ is $\\mathcal
  C^{2}$-smooth and locally pseudoconvex at every point\, then $\\Omega$ is
  globally pseudoconvex.  Unlike in the globally $\\mathcal C^{2}$-smooth 
 case\, the condition ``$F$ of (relative) empty interior'' is not enough to
 obtain such a result. \n\nhttps://indico.math.cnrs.fr/event/15247/
LOCATION:Amphi Schwartz
URL:https://indico.math.cnrs.fr/event/15247/
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