The Waist Inequality and Positive Scalar Curvature
[Virtual] Hot Topics: Regularity Theory for Minimal Surfaces and Mean Curvature Flow March 21, 2022 - March 24, 2022
Location: MSRI: Online/Virtual
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.