Macroscopic scalar curvature and areas of cycles

Hannah Alpert, Kei Funano

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we prove the following. Let Σ be an n–dimensional closed hyperbolic manifold and let g be a Riemannian metric on Σ × S1. Given an upper bound on the volumes of unit balls in the Riemannian universal cover (Σ × S1~ , g~) , we get a lower bound on the area of the Z2–homology class [ Σ × * ] on Σ × S1, proportional to the hyperbolic area of Σ. The theorem is based on a theorem of Guth and is analogous to a theorem of Kronheimer and Mrowka involving scalar curvature.

Original languageEnglish
Pages (from-to)727-743
Number of pages17
JournalGeometric and Functional Analysis
Volume27
Issue number4
DOIs
Publication statusPublished - 2017 Jul 1

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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