There is a conjecture that complete Riemannian 3-manifold with bounded sectional curvature, and pointwise pinched nonnegative Ricci must be flat or compact. We show this true when the negative part (if any) of curvature decays quadratically.

Abstract As ferroelectric Hf 0.5 Zr O 2 (HZO) thickness scales below 10 nm, the switching characteristics are severely distorted typically showing an antiferroelectric-like behavior (pinched hysteresis) with reduced remanent polarization. Using Landau-Ginsburg-Devonshire (LGD) theory for analysis of experimental results, it is shown here that, in thin (5 nm) HZO, depolarization fields drive sys...

We consider a totally nonsymplectic (TNS) Anosov action of Zk which is either uniformly quasiconformal or pinched on each coarse Lyapunov distribution. We show that such an action on a torus is C∞–conjugate to an action by affine automorphisms. We also obtain similar global rigidity results for actions on an arbitrary compact manifold assuming that the coarse Lyapunov foliations are topological...

In this paper, we prove a generalized integral inequality for submanifolds with parallel mean curvature vector in an arbitrary Riemannian manifold, and from which we obtain a pinching theorem for compact oriented submanifolds with parallel mean curvature vector in a complete simply connected pinched Riemannian manifold, which generalizes the results obtained by Alencar-do Carmo and Hong-Wei Xu.