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.

Wonder link: https://app.wonder.me/?spaceId=0ac77849-6011-43c1-85c1-55d02b5791c1

Meeting password: XHhrSLPzv6