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Oberseminar Differentialgeometrie: Rudolf Zeidler (WWU Münster), Vortrag: Scalar and mean curvature comparison via the Dirac operator

Monday, 26.04.2021 16:15 per ZOOM: Link to Zoom info

Mathematik und Informatik

Abstract: In recent years, Gromov proposed studying the geometry of positive scalar curvature ("psc'') via various metric inequalities vaguely reminiscent of classical comparison geometry. For instance, let $M$ be a closed manifold of dimension $n-1$ which does not admit a metric of psc. Then with respect to any Riemannian metric of scalar curvature $\geq n(n-1)$ on the cylinder $V = M \times [-1,1]$, the distance between the two boundary components of $V$ is conjectured to be at most $2\pi/n$. In this talk, we will discuss how to approach this and other related conjectures on spin manifolds via index-theoretic techniques. We will use variations of the spinor Dirac operator augmented by a Lipschitz potential and subject to suitable local boundary conditions. In the cases we consider, this leads to refined estimates involving the mean curvature of the boundary and to rigidity results for the extremal situation. Joint work with S. Cecchini.



Angelegt am Tuesday, 30.03.2021 11:17 von shupp_01
Geändert am Thursday, 15.04.2021 12:06 von shupp_01
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