d_p convergence and epsilon-regularity theorems for entropy and scalar curvature lower bound

Veranstalter: Institut für Analysis und Numerik

Donnerstag, 15.04.2021, 15:00-16:00

<p><span style="font-size: 10pt;">Am <strong>Donnerstag, den 15.04.2021 um 15:00 Uhr</strong> hält Dr. </span><span style="font-size: 8pt;"><span style="font-size: 10pt;"><strong>Man-Chun Lee</strong> (Northwestern University and University of Warwick) im Zoom Meeting einen Vortrag zum Thema:</span></span></p><p><strong><span style="font-size: 10pt;">d_p convergence and epsilon-regularity theorems for entropy and scalar curvature lower bound</span></strong></p><p class="p8" style="margin-bottom: 0.2in;"><span style="font-size: 10pt;"><strong>Abstract</strong>:</span></p><p class="p8" style="margin-bottom: 0.2in;"><span style="font-size: 10pt;"> In this talk, we consider Riemannian manifolds with almost non-negative scalar curvature and Perelman entropy. We establish an epsilon-regularity theorem showing that such a space must be close to Euclidean space in a suitable sense. We will illustrate examples showing that the result is false with respect to the Gromov-Hausdorff and Intrinsic Flat distances, and more generally the metric space structure is not controlled under entropy and scalar lower bounds. We will introduce the notion of the d_p distance between (in particular) Riemannian manifolds, which measures the distance between W^{1,p} Sobolev spaces, and it is with respect to this distance that the epsilon regularity theorem holds. This is joint work with A. Naber and R. Neumayer.</span></p><p> </p><p> </p>

Kontakt: Prof. Dr. Miles Simon

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Letzte Änderung: 13.03.2017 - Ansprechpartner: