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SUMMARY:Doubling inequalities for eigenfunctions - Eugenia Malinnikova (St
 anford University)
DTSTART:20260205T093000Z
DTEND:20260205T103000Z
UID:TALK239827@talks.cam.ac.uk
DESCRIPTION:Doubling inequalities quantify local growth properties of eige
 nfunctions\, bound their vanishing order\, and provide a basic quantitativ
 e form of unique continuation. They have become a standard tool in spectra
 l geometry and related PDE questions\, including bounds for nodal and sing
 ular sets. I will give an overview of doubling estimates for Laplace eigen
 functions on manifolds\, as well as various methods\, used in the proof of
  such inequalities: Carleman estimates in the tradition of Donnelly&ndash\
 ;Fefferman\, geometric arguments via harmonic extension/lift\, and a new p
 ropagation-of-smallness approach. If time permits\, I will briefly discuss
  boundary analogues and current work on doubling in the presence of conic 
 singularities.
LOCATION:Seminar Room 1\, Newton Institute
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