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NCTS Differential Geometry Seminar
 
20:00 - 21:00, May 26, 2022 (Thursday)
Wonder, Online seminar
(線上演講 Wonder)
Degeneration of 7-dimensional Minimal Hypersurfaces with Bounded Index
Nicholas Edelen (University of Notre Dame)

Abstract

A 7D minimal and locally-stable hypersurface will in general have a discrete singular set, provided it has no singularities modeled on a union of half-planes. We show in this talk that the geometry/topology/singular set of these surfaces has uniform control, in the following sense: if  is a sequence of 7D minimal hypersurfaces with uniformly bounded index and area, and discrete singular set, then up to a subsequence all the  are bi-Lipschitz equivalent, with uniform Lipschitz bounds on the maps. As a consequence, we prove the space of   embedded minimal hypersurfaces in a fixed -manifold, having index  , area  , and discrete singular set, divides into finitely-many diffeomorphism types.

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Meeting password: XHhrSLPzv6

 



 

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