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UID:385a996767715dafd87453f37f477500
CATEGORIES:Joint Princeton-Rutgers Seminar on Geometric PDE's
CREATED:20210524T105814
SUMMARY:Degeneration of 7-dimensional minimal hypersurfaces which are stable or have bounded index
LOCATION:zoom
DESCRIPTION:<p><strong style="background-color: inherit; color: inherit; font-family: i
 nherit; font-size: 1rem;">Abstract:&nbsp;</strong>A 7-dimensional area-mini
 mizing hypersurface $M$ can have in general a discrete singular set. The sa
 me is true if M is only locally-stable for the area-functional, provided $h
 aus^6(sing M) = 0$. In this paper we show that if $M_i$ is a sequence of 7D
  minimal hypersurfaces with discrete singular set which are minimizing, sta
 ble, or have bounded index, and varifold-converge to some $M$, then the geo
 metry, topology, and singular set of the $M_i$ can degenerate in only a ver
 y precise manner. We show that one can always ``parameterize'' a subsequenc
 e $i'$ by ambient, controlled bi-Lipschitz maps taking $phi_{i'}(M_1) = M_{
 i'}$. As a consequence, we prove that the space of closed, $C^2$ embedded m
 inimal hypersurfaces in a closed 8-manifold $(N, g)$ with a priori bounds $
 haus^7(M) leq Lambda$ and $index(M) leq I$ divides into finitely-many diffe
 omorphism types, and this finiteness continues to hold if one allows the me
 tric $g$ to vary, or $M$ to be singular.</p>
CONTACT:Nick Edelen, University of Notre Dame
X-EXTRAINFO:https://princeton.zoom.us/j/95636729444
DTSTAMP:20260921T040247
DTSTART;TZID=America/New_York:20210524T130000
DTEND;TZID=America/New_York:20210524T140000
SEQUENCE:0
TRANSP:OPAQUE
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