21 citations · 97 across the 20 of their papers we have counts for
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Product Inequalities for -Stabilized Scalar Curvature
Misha Gromov
We study metric invariants of Riemannian manifolds defined via the -stabilized scalar curvatures of manifolds mapped to and prove in some cases addit…
Isometric Immersions with Controlled Curvatures
Misha Gromov
We -approximate strictly short (e.g. constant) maps between Riemannin manifolds for by -smooth isometric immersions with c…
Curvature, Kolmogorov Diameter, Hilbert Rational Designs and Overtwisted Immersions
Misha Gromov
We prove the existence of locally distance increasing maps with it controllable small curvatures
Convex Polytopes, Dihedral Angles, Mean Curvature and Scalar Curvature
Misha Gromov
We approximate boundaries of convex polytopes by smooth hypersurfaces with {\it positive mean curvatures} and, by using basic geometric relations between the scal…
Scalar Curvature, Injectivity Radius and Immersions with Small Second Fundamental Forms
Misha Gromov
We prove in special cases the following. Bounds on the {\it injectivity radii} of "topologically complicated" Riemannian -manifolds , where the scalar curvatur…
Area and Gauss-Bonnet inequalities with scalar curvature
Misha Gromov, Jintian Zhu
Let be an -dimensional Riemannian manifold with "large positive" scalar curvature. In this paper, we prove in a variety of cases that if "spreads" in directions…
Torsion Obstructions to Positive Scalar Curvature
Misha Gromov, Bernhard Hanke
We study obstructions to the existence of Riemannian metrics of positive scalar curvature on closed smooth manifolds arising from torsion classes in the integral homology of their…
No metrics with Positive Scalar Curvatures on Aspherical 5-Manifolds
Misha Gromov
A metric space is called uniformly acyclic if there there exists an {\it acyclicty control function} , , such that the homology inclusion…
Four Lectures on Scalar Curvature
Misha Gromov
We overview main topics and ideas in spaces with their scalar curvatures bounded from below, and present a more detailed exposition of several known and some new geometric constrai…
Mean Curvature in the Light of Scalar Curvature
Misha Gromov
We formulate several conjectures on mean convex domains in the Euclidean spaces, as well as in more general spaces with lower bonds on their scalar curvatures, and prove a few theo…
Dirac and Plateau Billiards in Domains with Corners
Misha Gromov
We study metrics with positive scalar curvatures in domains with corners and suggest possible extensions of the concept of positive scalar curvature to singular spaces.
Plateau Stein Manifolds
Misha Gromov
We study/construct (proper and non-proper) Morse functions on complete Riemannian manifolds, the level hypersurfaces of which have positive mean curvatures at all non-critical poin…
Scalar Curvature of Manifolds with Boundaries: Natural Questions and Artificial Constructions
Misha Gromov
We present several problems and results relating the scalar curvatures of manifolds with mean curvatures of their boundaries
A Dozen Problems, Questions and Conjectures about Positive Scalar Curvature
Misha Gromov
We collect a few guesses on possible implications of a lower bound on the scalar curvature of a Riemannian manifold on the size and shape of this manifold.
Metric Inequalities with Scalar Curvature
Misha Gromov
We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below, in the spirit of the classical boun…