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SUMMARY:Area minimizing surfaces in mean convex 3-manifolds - Baris Coskun
 uzer (Koc University)
DTSTART:20120507T160000Z
DTEND:20120507T170000Z
UID:TALK37326@talks.cam.ac.uk
CONTACT:Jonathan Ben-Artzi
DESCRIPTION:In this talk\, we give several results on area minimizing surf
 aces in strictly mean convex 3-manifolds. First\, we study the genus of ab
 solutely area minimizing surfaces in a compact\, orientable\, strictly mea
 n convex 3-manifold M bounded by a simple closed curve in the boundary of 
 M. Our main result is that for any g>=0\, the space of simple closed curve
 s in the boundary of M where all the absolutely area minimizing surfaces t
 hey bound in M has genus >=g is open and dense in the space A of nullhomol
 ogous simple closed curves in the boundary of M. For showing this\, we pro
 ve a bridge principle for absolutely area minimizing surfaces. Moreover\, 
 we show that for any g>=0\, there exists a curve in A such that the minimu
 m genus of the absolutely area minimizing surfaces it bounds is exactly g.
  As an application of these results\, we further prove that the simple clo
 sed curves in the boundary of M bounding more than one minimal surface in 
 M is an open and dense subset of A. We also show that there are disjoint s
 imple closed curves in the boundary of M bounding minimal surfaces in M wh
 ich are not disjoint. This allows us to answer a question of Meeks\, by sh
 owing that for any strictly mean convex 3-manifold M\, there exists a simp
 le closed curve \\Gamma in the boundary of M which bounds a stable minimal
  surface which is not embedded. This is a joint work with Theodora Bourni.
LOCATION:CMS\, MR11
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