Curved Bistable Composite Slit Tubes with Positive Gaussian Curvature

of non-positive Gaussian curvature

α-Synuclein induces both positive mean curvature and negative Gaussian curvature in membranes.

Using a combination of X-ray scattering, fluorescence correlation spectroscopy, coarse-grained molecular dynamics (MD) simulations and potential of mean force calculations, we have explored the membrane remodeling effects of monomeric α-synuclein (αS). Our initial findings from multiple approaches are that αS (1) causes a significant thinning of the bilayer and (2) stabilizes positive mean curv...

Large bending deformations of pressurized curved tubes

In this paper, the problem of large pure bending deformations of membrane is considered. The membrane is a sector of torus with a closed cross-section. This membrane is called a curved tube for short. We consider the homogenous, incompressible, isotropic and hyperelastic material. The external load is a constant pressure and bending couples acting at the edges. The equilibrium equations reduce ...

Positive Scalar Curvature with Symmetry

We show an equivariant bordism principle for constructing metrics of positive scalar curvature that are invariant under a given group action. Furthermore, we develop a new codimension2 surgery technique which removes singular strata from fixed point free S-manifolds while preserving equivariant positive scalar curvature. These results are applied to derive the following generalization of a resu...

Slant Surfaces with Prescribed Gaussian Curvature

A slant immersion was introduced in [2] as an isometric immersion of a Riemannian manifold into an almost Hermitian manifold (M̃, g, J) with constant Wirtinger angle. From J-action point of view, the most natural surfaces in an almost Hermitian manifold are slant surfaces. Flat slant surfaces in complex space forms have been studied in [3, 4]. In this article, we study slant surfaces in complex ...