The Borel Conjecture predicts that closed aspherical manifolds are topological rigid. We want to investigate when a non-aspherical oriented connected closed manifold M is topological rigid in the following sense. If f : N → M is an orientation preserving homotopy equivalence with a closed oriented manifold as target, then there is an orientation preserving homeomorphism h : N → M such that h an...

We consider a prototypical "stretching plus bending" functional of an elastic shell. The shell is modeled as d-dimensional Riemannian manifold endowed, in addition to the metric, with reference second fundamental form. immersed into (d+1)-dimensional ambient space, and energy accounts for deviations induced metric forms from their values. Under assumption that space constant sectional curvature...

In this survey paper, we outline the proofs of the rigidity results (Mostow type, quasi-isometric, and Diagram rigidity) for simple, thick, hyperbolic P-manifolds found in [L1], [L2], [L3]. The later spaces are in some sense the simplest non-manifold locally CAT(1) spaces one can create. All the proofs depend on the highly non-homogenous structure of the boundary at infinity of the (universal c...

In this Letter, we consider a neutral system of mobile positive and negative charges confined on the surface of curved films. This may be an appropriate model for: i) a highly charged membrane whose counterions are confined to a sheath near its surface; ii) a membrane composed of an equimolar mixture of anionic and cationic surfactants in aqueous solution. We find that the charge fluctuations c...

Parkinson's disease (PD) is associated with motor and non-motor rigidity symptoms (e.g., cognitive and personality). The question is raised as to whether rigidity in PD also extends to perception, and if so, whether perceptual, cognitive, and personality rigidities are correlated. Bistable stimuli were presented to 28 non-demented individuals with PD and 26 normal control adults (NC). Necker cu...

The geometry of cavities in the surfaces of proteins facilitates a variety of biochemical functions. To better understand the biochemical nature of protein cavities, the shape, size, chemical properties, and evolutionary nature of functional and nonfunctional surface cavities have been exhaustively surveyed in protein structures. The rigidity of surface cavities, however, is not immediately ava...