Scalar Curvature and Betti Numbers of Compact Riemannian Manifolds

2019 ◽  
Vol 51 (3) ◽  
pp. 761-771
Author(s):  
Hezi Lin
Keyword(s):  
Scalar Curvature ◽  
Riemannian Manifolds ◽  
Betti Numbers

scholarly journals Volume and macroscopic scalar curvature

2021 ◽  
Author(s):  
Sabine Braun ◽  
Roman Sauer
Keyword(s):  
Riemannian Manifold ◽  
Scalar Curvature ◽  
Riemannian Manifolds ◽  
Upper Bound ◽  
Betti Numbers ◽  
Universal Cover ◽  
Positive Scalar Curvature ◽  
Simplicial Volume ◽  
Positive Scalar ◽  
Curvature Bound

AbstractWe prove the macroscopic cousins of three conjectures: (1) a conjectural bound of the simplicial volume of a Riemannian manifold in the presence of a lower scalar curvature bound, (2) the conjecture that rationally essential manifolds do not admit metrics of positive scalar curvature, (3) a conjectural bound of $$\ell ^2$$ ℓ 2 -Betti numbers of aspherical Riemannian manifolds in the presence of a lower scalar curvature bound. The macroscopic cousin is the statement one obtains by replacing a lower scalar curvature bound by an upper bound on the volumes of 1-balls in the universal cover.

Sewing Riemannian Manifolds with Positive Scalar Curvature

2017 ◽  
Vol 28 (4) ◽  
pp. 3553-3602 ◽  
Author(s):  
J. Basilio ◽  
J. Dodziuk ◽  
C. Sormani
Keyword(s):  
Scalar Curvature ◽  
Riemannian Manifolds ◽  
Positive Scalar Curvature ◽  
Positive Scalar

Prescribing the Scalar Curvature Problem on Three and Four Manifolds

2003 ◽  
Vol 3 (4) ◽  
Author(s):  
Hichem Chtioui
Keyword(s):  
Scalar Curvature ◽  
Riemannian Manifolds ◽  
Critical Points ◽  
New Class ◽  
Critical Points At Infinity ◽  
Four Manifolds ◽  
Curvature Problem

AbstractThis paper is devoted to the prescribed scalar curvature problem on 3 and 4- dimensional Riemannian manifolds. We give a new class of functionals which can be realized as scalar curvature. Our proof uses topological arguments and the tools of the theory of the critical points at infinity.

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