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Four Lectures on Scalar Curvature

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arxiv 1908.10612 v6 pith:6DX23NL4 submitted 2019-08-28 math.DG

Misha Gromov This is my paper · ORCID
classification math.DG
keywords scalarcurvaturesspacesbelowboundedboundsconstraintscurvature
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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 constraints on Riemannian spaces implied by the lower bounds on their scalar curvatures

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Rosenberg $ \mathbb{S}^{1} $-Stability Conjecture for $ \chi(X) = 0 $

    math.DG 2026-07 conditional novelty 7.0 of 10

    For closed oriented manifolds X with dim X ≥ 5 and χ(X)=0, the Rosenberg S¹-stability conjecture holds: X × S¹ admits a PSC metric if and only if X does.

  2. Connected sum of manifolds with spectral Ricci lower bounds

    math.DG 2025-05 conditional novelty 7.0 of 10

    Connected sums preserve the spectral Ricci bound lambda1(-gamma Delta + Ric) > lambda for n >= 3 and gamma > (n-1)/(n-2), and this range is sharp.

  3. Abstract cone operators and Lipschitz rigidity for scalar curvature on singular manifolds

    math.DG 2025-05 accept novelty 7.0 of 10

    Odd-dimensional Llarull rigidity holds for Lipschitz area non-increasing maps and for manifolds with cone-like singularities, proved via spherical suspension and abstract cone operators.

  4. Codimension 2 drawstrings with scalar curvature lower bounds

    math.DG 2025-01 conditional novelty 7.0 of 10

    Kazaras and Xu construct drawstring metrics along arbitrary codimension-2 submanifolds with scalar curvature almost bounded below, yielding new collapsed limits and a claimed but flawed Llarull counterexample.

  5. On the rigidity of manifolds with respect to Gagliardo-Nirenberg inequalities

    math.DG 2025-07 conditional novelty 6.0 of 10

    Certain Gagliardo-Nirenberg and unweighted Yamabe-type constant comparisons force open Riemannian sets to be flat.

  6. Scalar and Mean Curvature Comparison on Compact Cylinder

    math.DG 2025-07 conditional novelty 5.0 of 10

    On a compact cylinder X×I with positive scalar curvature and nonnegative mean curvature, the angle condition guarantees existence of a metric with positive scalar curvature on X, forcing negative mean curvature if X a...

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