scholarly journals Scalar Curvature Bound for Kahler-Ricci Flows over Minimal Manifolds of General Type

2009 ◽  
Author(s):  
Z. Zhang
Keyword(s):  
Scalar Curvature ◽  
General Type ◽  
Curvature Bound ◽  
Ricci Flows

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.

scholarly journals SEIBERG–WITTEN EQUATIONS ON SURFACES OF LOGARITHMIC GENERAL TYPE

2013 ◽  
Vol 24 (09) ◽  
pp. 1350074
Author(s):  
LUCA FABRIZIO DI CERBO
Keyword(s):  
Lower Bound ◽  
Scalar Curvature ◽  
General Type ◽  
Einstein Metrics ◽  
Existence Results

We study the Seiberg–Witten (SW) equations on surfaces of logarithmic general type. First, we show how to construct irreducible solutions of the SW equations for any metric which is "asymptotic" to a Poincaré type metric at infinity. Then we compute a lower bound for the L2-norm of scalar curvature on these spaces and give non-existence results for Einstein metrics on blow-ups.

scholarly journals Scalar Curvature Behavior of Homogeneous Ricci Flows

2014 ◽  
Vol 25 (4) ◽  
pp. 2313-2322 ◽  
Author(s):  
Ramiro A. Lafuente
Keyword(s):  
Scalar Curvature ◽  
Ricci Flows
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