Communications in Analysis and Geometry
Volume 30 (2022)
Macroscopic stability and simplicial norms of hypersurfaces
Pages: 949 – 959
We introduce a $Z$-coefficient version of Guth’s macroscopic stability inequality for almost-minimizing hypersurfaces. In manifolds with a lower bound on macroscopic scalar curvature, we use the inequality to prove a lower bound on areas of hypersurfaces in terms of the Gromov simplicial norm of their homology classes. We give examples to show that a very positive lower bound on macroscopic scalar curvature does not necessarily imply an upper bound on the areas of minimizing hypersurfaces.
Received 26 December 2017
Accepted 8 November 2019
Published 17 March 2023