We consider Lorentz surfaces in R13 satisfying the condition H2−K≠0, where K and H are Gaussian curvature mean curvature, respectively, call them of general type. For this class surfaces, we introduce special isotropic coordinates, which canonical, show that coefficient F first fundamental form H, expressed terms canonical satisfy a integro-differential equation natural Using equation, prove th...

In this paper we discuss models satisfying the limiting curvature condition. For purpose modify Einstein-Hilbert action by adding a term which restricts growth of curvature. We analyze cosmological solutions in such models. Namely, consider closed contracting homogeneous isotropic universe filled with thermal radiation. demonstrate that for properly chosen constraints has bounce. As result its ...

Soft materials with layered structure such as membranes, block copolymers and smectics exhibit intriguing morphologies with nontrivial curvatures. Here, we report restructuring the Gaussian and mean curvatures of smectic A films with free surface in the process of sintering, that is, reshaping at elevated temperatures. The pattern of alternating patches of negative, zero and positive mean curva...

Let Fm = (M,F ) be a Finsler manifold and G be the Sasaki– Finsler metric on the slit tangent bundle TM0 = TM {0} of M . We express the scalar curvature ρ̃ of the Riemannian manifold (TM0, G) in terms of some geometrical objects of the Finsler manifold Fm. Then, we find necessary and sufficient conditions for ρ̃ to be a positively homogenenous function of degree zero with respect to the fiber coo...

In this paper we investigate a family of partial di erential equations (PDEs) for image processing which can be regarded as isotropic nonlinear di usion with an additional factor on the right-hand side. The one-dimensional analogues to this lter class have been motivated as scaling limits of one-dimensional adaptive averaging schemes. In 2-D, mean curvature motion is one of the most prominent e...

In this paper, we propose a new scheme for anisotropic motion by mean curvature in R. The scheme consists of a phase-field approximation of the motion, where the nonlinear diffusive terms in the corresponding anisotropic Allen-Cahn equation are linearized in the Fourier space. In real space, this corresponds to the convolution with a specific kernel of the form Kφ,t(x) = F−1 [ e−4π 2tφo(ξ) ] (x...

Nonlamellar lipid membranes are frequently induced by proteins that fuse, bend, and cut membranes. Understanding the mechanism of action of these proteins requires the elucidation of the membrane morphologies that they induce. While hexagonal phases and lamellar phases are readily identified by their characteristic solid-state NMR line shapes, bicontinuous lipid cubic phases are more difficult ...