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SUMMARY:Pfaffian systems and the fundamental theorem of surface theory - F
 lorian Litzinger\, Queen Mary University of London
DTSTART:20190221T160000Z
DTEND:20190221T170000Z
UID:TALK120391@talks.cam.ac.uk
CONTACT:Angeliki Menegaki
DESCRIPTION:The fundamental theorem of surface theory states that there ex
 ists an immersion of a surface in three-dimensional space with prescribed 
 first and second fundamental forms whenever the given forms satisfy the Ga
 uß–Codazzi–Mainardi equations. The proof is based on the solution of 
 a Pfaffian system\, which is a system of first-order linear PDE\, and an \
 napplication of the Poincaré lemma. Consequently\, the regularity of the 
 resulting immersion crucially depends on the regularity of the solution of
  the corresponding Pfaffian system. This talk shall give an introduction t
 o the classical smooth case\, the existing regularity theory\, and a possi
 ble extension to the optimal regularity.
LOCATION:MR14\, Centre for Mathematical Sciences
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