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SUMMARY:Bumpy Metrics for Minimal Submanifolds - Paul Minter (University o
 f Cambridge)
DTSTART:20200130T163000Z
DTEND:20200130T173000Z
UID:TALK139075@talks.cam.ac.uk
CONTACT:Renato Velozo
DESCRIPTION:Consider the 2-sphere in Euclidean 3-space with the usual roun
 d metric\, where we know the geodesics are arcs of great circles. By rotat
 ion we get a 1-parameter family of geodesics through any given geodesic\, 
 which turns out to imply that each geodesic is degenerate for the length f
 unctional since it then has a non-trivial Jacobi field. However if we chan
 ge the metric on the 2-sphere to\, say\, that of a triaxial ellipsoid\, al
 l but 3 of these closed geodesics disappear. Perturbing the metric further
  via adding more "bumps" to the 2-sphere\, all geodesics are in fact non-d
 egenerate.  In 1970 Ralph Abraham established that on a compact manifold\,
  'almost all' metrics have the property that any geodesic is non-degenerat
 e. This result was then extended to the case of minimal submanifolds of an
 y codimension in 1991 by Brian White to a result now known as the Bumpy Me
 trics Theorem. In this talk we shall discuss the Bumpy Metrics Theorem\, a
 nd then some conjectures we have for extending it to the case of singular 
 hypersurfaces.
LOCATION:MR14\, Centre for Mathematical Sciences
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