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SUMMARY:Minimal Graphs in Arbitrary Codimension - Spencer Hughes (CCA)
DTSTART:20140521T150000Z
DTEND:20140521T160000Z
UID:TALK52390@talks.cam.ac.uk
CONTACT:Vittoria Silvestri
DESCRIPTION:The minimal surface equation is the prototypic example of a no
 nlinear (quasilinear to be precise) second order elliptic PDE. It has been
  studied in depth and as such a lot is known about graphical minimal subma
 nifolds in codimension one (the geometric objects which the equation descr
 ibes). By contrast\, relatively little is known about graphical minimal su
 bmanifolds in higher codimension. This lack of knowledge is in some sense 
 'explained' by the failure of standard\, desirable PDE results for the min
 imal surface system\, all of which is described in the wonderfully titled 
 1977 paper of Lawson and Osserman: "Non-existence\, non-uniqueness and irr
 egularity of solutions to the minimal surface system". The reality of cour
 se is that the failure of the standard results opens up many much more int
 eresting questions\, many of which are still open. I intend to sketch some
  less common proofs of well-known facts in the codimension one case\, disc
 uss whether or not they generalize to higher codimension and then possibly
  make some conjectures.
LOCATION:MR14\, Centre for Mathematical Sciences
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