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
![](https://chart.googleapis.com/chart?cht=tx&chl=%24M_i%24&chf=bg,s,333333&chco=ffffff)
is a sequence of 7D minimal hypersurfaces with uniformly bounded index and area, and discrete singular set, then up to a subsequence all the
![](https://chart.googleapis.com/chart?cht=tx&chl=%24M_i%24&chf=bg,s,333333&chco=ffffff)
are bi-Lipschitz equivalent, with uniform Lipschitz bounds on the maps. As a consequence, we prove the space of
![](https://chart.googleapis.com/chart?cht=tx&chl=%24C%5E2%24&chf=bg,s,333333&chco=ffffff)
embedded minimal hypersurfaces in a fixed
![](https://chart.googleapis.com/chart?cht=tx&chl=%248%24&chf=bg,s,333333&chco=ffffff)
-manifold, having index
![](https://chart.googleapis.com/chart?cht=tx&chl=%24%5Cleq%20I%24&chf=bg,s,333333&chco=ffffff)
, area
![](https://chart.googleapis.com/chart?cht=tx&chl=%24%5Cleq%20%5CLambda%24&chf=bg,s,333333&chco=ffffff)
, and discrete singular set, divides into finitely-many diffeomorphism types.
Link information
Meeting password: XHhrSLPzv6