In this paper we continue our study of finding the curvature flow of complete hypersurfaces in hyperbolic space with a prescribed asymptotic boundary at infinity. Our main results are proved by deriving a priori global gradient estimates and C2 estimates.

This paper presents a rank rigidity result for negatively curved spaces. Let M be a compact manifold with negative sectional curvature and suppose that along every geodesic in M there is a parallel vector field making curvature −a with the geodesic direction. We prove that M has constant curvature equal to −a if M is odd dimensional, or if M is even dimensional and has sectional curvature pinch...

We show that noncompact homogeneous spaces not diffeomorphic to Euclidean space of dimension 9 or 10 admit no Einstein metrics negative Ricci curvature, with only three potential exceptions. The main ingredient in the proof is show, via a cohomogeneity-one approach, admitting an ideal isomorphic $ \mathfrak{sl}_2(\mathbb{R}) curvature.

In this paper energy bands and Berry curvature of graphene was studied. Desired Hamiltonian regarding the next-nearest neighbors obtained by tight binding model. By using the second quantization approach, the transformation matrix is calculated and the Hamiltonian of system is diagonalized. With this Hamiltonian, the band structure and wave function can be calculated. By using calculated wave f...

Deformations of cell membranes, such as fusion, adhesion, budding, and pore formation, play important roles in the maintenance of living cell systems. In cell systems, the membrane deformations are managed by complex interplays between membrane proteins and lipids. It is hypothesized that one role of the membrane proteins is to introduce a local spontaneous curvature by interacting with the mem...

in this study the land surface in western half of hyper-arid lut desert, in south east of iran, which is covered by yardangs, a worldwide typical landform for aeolian erosion, were classified by self organizing maps (som) method. in the first step by using digital elevation model with 10 m resolution and matlab software, 22 morphometric parameters were calculated based on derivative of the surf...

INTRODUCTION We describe a new surgical technique for the treatment of penile curvature that combines features of the Nesbit procedure with features of tunical plication. U-shaped flaps of tunica albuginea are freed from the corpus cavernosum. The flaps are brought under the remaining tunica albuginea and are fixated with single absorbable sutures. As the defects of the tunica are sealed tightl...