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SUMMARY:Minimizing the area of the Gauss map of surfaces in S3 - Gerard Or
 riols\, University of Cambridge
DTSTART:20251110T140000Z
DTEND:20251110T150000Z
UID:TALK236731@talks.cam.ac.uk
CONTACT:Giacomo Ageno
DESCRIPTION:For a closed embedded surface in the round 3-sphere\, one can 
 consider its Gauss map taking values in the Grassmannian of 2-planes in 4-
 space\, and try to minimize its area among all surfaces of a given genus. 
 We will present some motivations to study this functional\, its relation t
 o other variational problems\, and a dichotomy between spheres\, for which
  the infimum is achieved\, and surfaces of genus g>0\, for which there are
  no minimizers and minimizing sequences must degenerate. After describing 
 some interesting ways in which this degeneration can occur\, giving rise t
 o a round sphere and g-1 small handles where the negative curvature concen
 trates\, we will present a compactness result showing roughly that all mi
 nimizing sequences exhibit that behaviour. This is based on joint work wit
 h T. Riviere.
LOCATION:Lecture Room 2 in the gatehouse at INI.
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