Gaussian Curvature as an Identifier of Shell Rigidity

Rigidity in Non-negative Curvature

In this paper we will show that any complete manifold of nonnegative curvature has a flat soul provided it has curvature going to zero at infinity. We also show some similar results about manifolds with bounded curvature at infinity. To establish these theorems we will prove some rigidity results for Riemannian submersions, eg., any Riemannian submersion with complete flat total space and compa...

Measure Rigidity of Ricci Curvature Lower Bounds

The measure contraction property, MCP for short, is a weak Ricci curvature lower bound conditions for metric measure spaces. The goal of this paper is to understand which structural properties such assumption (or even weaker modifications) implies on the measure, on its support and on the geodesics of the space. We start our investigation from the euclidean case by proving that if a positive Ra...

of non-positive Gaussian curvature

On Mostow rigidity for variable negative curvature

We prove a finiteness theorem for the class of complete finite volume Riemannian manifolds with pinched negative sectional curvature, fixed fundamental group, and of dimension ≥ 3. One of the key ingredients is that the fundamental group of such a manifold does not admit a small nontrivial action on an R -tree.

nano-rods zno as an efficient catalyst for the synthesis of chromene phosphonates, direct amidation and formylation of amines

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