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SUMMARY:Thomas Schick (University of Göttingen)
DTSTART:20201117T131500Z
DTEND:20201117T144500Z
DTSTAMP:20260422T151945Z
UID:GoeTop/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GoeTop/12/">
 Flexibility and Rigidity of Lipschitz Riemannian Geometry</a>\nby Thomas S
 chick (University of Göttingen) as part of Göttingen topology and geomet
 ry seminar\n\n\nAbstract\nEvery smooth isometric embedding of the 2-sphere
  into\n$\\mathbb{R}^3$ the standard one (upto rotations\, translations\, a
 nd reflections).\n\nIn contrast to this classical rigidity result we have 
 flexibility:\nThere are Lipschitz isometric embeddings of the 2-sphere in 
 $\\mathbb{R}^3$ whose image\nhas arbitrarily small diameter.\n\nThe talk w
 ill present more of these surprising flexibility results for\nLipschitz ma
 ps between Riemannian manifolds.\n\nEventually\, our focus will be on the 
 following rigidity result of Llarull:\n\nlet $f\\colon M \\to S^n$ be a sm
 ooth map between a compact Riemannian manifold M and\nS^n with the standar
 d metric. If M is sufficiently curved (scalar\ncurvature is everywhere >= 
 the scalar curvature of $S^n$)\, if the map is\nnon-expanding (Lipschitz c
 onstant <=1) and if it is far enough from a constant\nmap (has non-zero de
 gree) then f must be an isometry.\n\nWe will discuss the ideas of the proo
 f\, which involve the geometry of vector\nbundles\, and Gromov's question 
 whether rigidity prevails or flexibility occurs\nif just have Lipschitz co
 ntinuity in the setup of the above theorem.\n
LOCATION:https://researchseminars.org/talk/GoeTop/12/
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