Metric Inequalities with Scalar Curvature

Misha Gromov

Research output: Contribution to journalArticlepeer-review


We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below. In so far as geometry is concerned these inequalities appear as generalisations of the classical bounds on the distances between conjugates points in surfaces with positive sectional curvatures. The techniques of our proofs is based on the Schoen–Yau descent method via minimal hypersurfaces, while the overall logic of our arguments is inspired by and closely related to the torus splitting argument in Novikov’s proof of the topological invariance of the rational Pontryagin classes.

Original languageEnglish (US)
Pages (from-to)645-726
Number of pages82
JournalGeometric and Functional Analysis
Issue number3
StatePublished - Jun 1 2018

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology


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