Systolic inequalities and the Horowitz-Myers conjecture

Abstract: I will discuss joint work with Pei-Ken Hung on the Horowitz-Myers conjecture in dimension at most 7. Our approach relies on a new geometric inequality. For a Riemannian metric on $B^2 \times T^{n-2}$ with scalar curvature at least $-n(n-1)$, this inequality relates the systole of the boundary to the mean curvature of the boundary.

general relativity and quantum cosmologymathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

JoMaReC - Joint Online Mathematical Relativity Colloquium

Series comments: This monthly online colloquium is meant to be accessible to and informative for mathematicians and mathematical physicists with a background in General Relativity, widely interpreted to include Lorentzian Geometry, and Geometric Analysis of various Partial Differential Equations related to General Relativity.

It is aimed to present motivation and applications of particular results and/or introduce specific subfields, while refraining from too much technicalities.