Hannah Alpert

Ohio State University

March 12, 2019

A decades-old application of the second variation formula

proves that if the scalar curvature of a closed 3--manifold is bounded

below by that of the product of the hyperbolic plane with the line,

then every 2--sided stable minimal surface has area at least that of

the hyperbolic surface of the same genus. We can prove a coarser

analogue of this statement, taking the appropriate notions of

macroscopic scalar curvature and macroscopic minimizing hypersurface

from Guth's 2010 proof of the systolic inequality for the

n--dimensional torus. The appropriate analogue of hyperbolic area in

this setting turns out to be the Gromov simplicial norm. Joint work

with Kei Funano.