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SUMMARY:A sharp strong maximum principle for singular minimal hypersurface
 s - Neshan Wickramasekera (Cambridge)
DTSTART:20130603T140000Z
DTEND:20130603T150000Z
UID:TALK45671@talks.cam.ac.uk
CONTACT:Filip Rindler
DESCRIPTION:If two smooth\, connected\, embedded minimal hypersurfaces wit
 h no\nsingularities satisfy the property that locally near every common po
 int $p$\, one hypersurface lies on one side of the other\, then it is a di
 rect consequence of the Hopf maximum principle that either the hypersurfac
 es are disjoint or they coincide. Given that singularities in minimal hype
 rsurfaces are generally unavoidable\, it is a natural question to ask if t
 he same result must extend to pairs of singular minimal hypersurfaces (sta
 tionary codimesion 1 integral varifolds) with connected supports\; in this
  case the above ``one hypersurface lies locally on one side of the other''
  hypothesis can naturally be imposed for each common point $p$ which is a 
 regular point of at least one hypersurface.\n\nThe answer to this question
  in general is no in view of simple examples such as two pairs of transver
 sely interecting hyperplanes with a common axis. The answer however is yes
  if the singular set of one of the hypersurfaces has $(n-1)$-dimesional Ha
 usdorff measure zero\, where $n$ is the dimension of the hypersurfaces. I 
 will discuss this result\, which generalizes and unifies previous maximum 
 principles of Ilmanen and Solomon-White (and thereby unifies all previousl
 y known strong maximum principles for singular minimal hypersurfaces).
LOCATION:CMS\, MR13
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