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SUMMARY:Eigenvalue Estimates and Geometric Rigidity of Hypersurfaces - Abh
 itosh Upadhyay (Indian Institute of Technology)
DTSTART:20260205T163500Z
DTEND:20260205T165000Z
UID:TALK241582@talks.cam.ac.uk
DESCRIPTION:In this talk\, I will begin with a brief review of some founda
 tional geometric inequalities for hypersurfaces in Euclidean spaces focusi
 ng on those where equality charaacterizes the standared geodesic spheres. 
 A prime example is Reilly's celebraated inequality which provides a sharp 
 upper bound for the first non trivial eigenvalue of the Laplace Beltrami-o
 perator on compact\, embedded hypersurfaces. Interestingly\, these inequal
 ities can often be traced back to a fundamental estimate involving the $L^
 2$ norm of the position vector. I will then delve into a novel stability r
 efinement of this inequality: we establish that if a hypersurface nearly a
 ttains this lower bound on the $L^2$-norm\, then it must be geometrically 
 close\, in a suitable sense\, to a round sphere.
LOCATION:Seminar Room 1\, Newton Institute
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