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SUMMARY:Regularity theory for branched stable hypersurfaces - Paul Minter 
 (Cambridge)
DTSTART:20220307T140000Z
DTEND:20220307T150000Z
UID:TALK170951@talks.cam.ac.uk
CONTACT:Dr Greg Taujanskas
DESCRIPTION:In the 1960's\, Almgren developed a min-max theory for constru
 cting weak critical points of the area functional in arbitrary closed Riem
 annian manifolds. The regularity theory for these weak solutions (known as
  stationary integral varifolds) has been a fundamental open question in ge
 ometric analysis ever since. The primary difficulty arises from the possib
 ility of a type of degenerate singularity\, known as a branch point\, bein
 g present in the varifold. Allard (1972) was able to prove that the branch
  points form a closed nowhere dense subset\; however\, nothing is known re
 garding its size or local structure.\n\nIn this talk we will discuss recen
 t work (joint with N. Wickramsekera) regarding what can be said about the 
 local structure at a branch point. More precisely\, we prove local structu
 ral results about branch points in a large class of stationary integral va
 rifolds: those which are codimension one\, stable\, and do not contain cer
 tain so-called classical singularities. These results are directly applica
 ble to area minimising hypersurfaces mod p\, and resolve an old question f
 rom the work of B. White in this setting.
LOCATION:CMS\, MR13
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