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Geometric Analysis Seminar

The Waist Inequality and Positive Scalar Curvature

Davi Maximo - University of Pennsylvania

Location:  Zoom
Date & time: Tuesday, 06 April 2021 at 2:50PM - 3:50PM

Abstract: The topology of three-manifolds with positive scalar curvature has been (mostly) known since the solution of the Poincare conjecture by Perelman. Indeed, they consist of connected sums of spherical space forms and S^2 x S^1's. In spite of this, their "shape" remains unknown and mysterious. Since a lower bound of scalar curvature can be preserved by a codimension two surgery, one may wonder about a description of the shape of such manifolds based on a codimension two data (in this case, 1-dimensional manifolds).

In this talk, I will show results from a recent collaboration with Y. Liokumovich elucidating this question for closed three-manifolds.

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