Metric Inequalities with Scalar Curvature
By Misha Gromov. Geometric and Functional Analysis, 2017
162 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/37bba45c83f872910e9a237a0969821d1b9bc2d5
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In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- Width estimate and doubly warped product (2020, background): “In his paper [3], Gromov introduced the following definition.”