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CATEGORIES:Partial Differential Equations seminar
SUMMARY:Regularity theory for branched stable hypersurface
s - Paul Minter (Cambridge)
DTSTART;TZID=Europe/London:20220307T140000
DTEND;TZID=Europe/London:20220307T150000
UID:TALK170951AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/170951
DESCRIPTION:In the 1960's\, Almgren developed a min-max theory
for constructing weak critical points of the area
functional in arbitrary closed Riemannian manifol
ds. The regularity theory for these weak solutions
(known as stationary integral varifolds) has been
a fundamental open question in geometric analysis
ever since. The primary difficulty arises from th
e possibility of a type of degenerate singularity\
, known as a branch point\, being present in the v
arifold. Allard (1972) was able to prove that the
branch points form a closed nowhere dense subset\;
however\, nothing is known regarding its size or
local structure.\n\nIn this talk we will discuss r
ecent work (joint with N. Wickramsekera) regarding
what can be said about the local structure at a b
ranch point. More precisely\, we prove local struc
tural results about branch points in a large class
of stationary integral varifolds: those which are
codimension one\, stable\, and do not contain cer
tain so-called classical singularities. These resu
lts are directly applicable to area minimising hyp
ersurfaces mod p\, and resolve an old question fro
m the work of B. White in this setting.
LOCATION:CMS\, MR13
CONTACT:Dr Greg Taujanskas
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