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SUMMARY:Robin Neumayer (Northwestern)
DTSTART:20210316T134500Z
DTEND:20210316T144500Z
DTSTAMP:20260423T005650Z
UID:BOWL/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BOWL/18/">$d
 _p$ Convergence and $\\varepsilon$-regularity theorems for entropy and sca
 lar curvature lower bounds</a>\nby Robin Neumayer (Northwestern) as part o
 f B.O.W.L Geometry Seminar\n\n\nAbstract\nIn this talk\, we consider Riema
 nnian manifolds with almost non-negative scalar curvature and Perelman ent
 ropy. We establish an $\\varepsilon$-regularity theorem showing that such 
 a space must be close to Euclidean space in a suitable sense. Interestingl
 y\, such a result is false with respect to the Gromov-Hausdorff and Intrin
 sic Flat distances\, and more generally the metric space structure is not 
 controlled under entropy and scalar lower bounds. Instead\, we introduce t
 he notion of the $d_p$ distance between (in particular) Riemannian manifol
 ds\, which measures the distance between $W^{1\,p}$ Sobolev spaces\, and i
 t is with respect to this distance that the epsilon regularity theorem hol
 ds. We will discuss various applications to manifolds with scalar curvatur
 e and entropy lower bounds\, including a compactness and limit structure t
 heorem for sequences\, a uniform $L^\\infty$ Sobolev embedding\, and a pri
 ori $L^p$ scalar curvature bounds for $p<1$. This is joint work with Man-C
 hun Lee and Aaron Naber.\n
LOCATION:https://researchseminars.org/talk/BOWL/18/
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