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UID:8412@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20140331T100000
DTEND;TZID=Europe/Paris:20140331T110000
DTSTAMP:20241120T210405Z
URL:https://www.i2m.univ-amu.fr/evenements/on-the-regularity-of-mappings-a
 rising-from-solutions-of-tangent-cauchy-riemann-pdes/
SUMMARY:Ilya Kossovskiy (University of Vienna\, Austria): On the regularity
  of mappings\, arising from solutions of tangent Cauchy-Riemann PDEs
DESCRIPTION:Ilya Kossovskiy: One can define functions holomorphic on open s
 ets in Cn as smooth functions\, annihilated by the Cauchy-Riemann operator
   . Similarly\, one can consider smooth functions on a real submanifold M 
 of $\\CC{n}$\, annihilated by the naturally defined on M tangent Cauchy-Ri
 emann operator. The corresponding objects are called CR-functions on M. CR
 -functions naturally occur in complex analysis as restrictions of holomorp
 hic functions onto a real submanifold M\, and also as boundary values of f
 unctions\, holomorphic in a domain. A remarkable property of CR-functions 
 is their wedge holomorphic extension\, provided the CR-manifold M satisfie
 s certain nondegeneracy conditions (Tumanov\, 1980’s). Another remarkabl
 e property is the analyticicty of CR-diffeomorphisms between nondegenerate
  real-analytic submanifolds M\,M′ in Cn (i.e.\, CR-mappings in this case
  appear to be simply restrictions of holomorphic mappings). It was an open
  problem for a while whether one can drop the nondegeneracy conditions\, p
 osed on M and M′. In this talk we provide a negative answer for this que
 stion. Our construction is based on a connection between geometry of degen
 erate (more precisely\, nonminimal) real hypersurfaces in C2 and that of s
 econd order singular holomorphic differential equations. \n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 021/04/Ilya_Kossovskiy.jpg
CATEGORIES:Séminaire,Analyse et Géométrie
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