OBJECTIVE Cervical ossification of the posterior longitudinal ligament (OPLL) can be treated via anterior or posterior approach, or both. The optimal approach depends on the characteristics of OPLL and cervical curvature. Although most patients can be successfully treated by a single surgery with the proper approach, renewed or newly developed neurological deterioration often requires repeat su...

in this paper, we study spacelike dual biharmonic curves. we characterize spacelike dual biharmonic curves in terms of their curvature and torsion in the lorentzian dual heisenberg group . we give necessary and sufficient conditions for spacelike dual biharmonic curves in the lorentzian dual heisenberg group . therefore, we prove that all spacelike dual biharmonic curves are spacelike dual heli...

The main result of the paper is a computation of the Ricci curvature of Diff(S)/S. Unlike earlier results on the subject, we do not use the Kähler structure symmetries to compute the Ricci curvature, but rather rely on classical finite-dimensional results of Nomizu et al on Riemannian geometry of homogeneous spaces. Table of

In 25 eyes, age range 60-80 years, in purpose of preoperative treatment prior to cataract surgery, measurements of the radius of curvature as well as main meridians of the anterior and posterior corneal surfaces were performed. Average value of the curvature of the anterior corneal surface (R1) was R1 = 7.84 mm, while posterior radius (R2) was 6.4 mm. Main meridian of the anterior corneal surfa...

Thurston’s circle packing approximation of the Riemann Mapping (proven to give the Riemann Mapping in the limit by Rodin-Sullivan) is largely based on the theorem that any topological disk with a circle packing metric can be deformed into a circle packing metric in the disk with boundary circles internally tangent to the circle. The main proofs of the uniformization use hyperbolic volumes (Andr...

In this paper, using the local Ricci flow, we prove the short-time existence of the Ricci flow on noncompact manifolds, whose Ricci curvature has global lower bound and sectional curvature has only local average integral bound. The short-time existence of the Ricci flow on noncompact manifolds was studied by Wan-Xiong Shi in 1990s, who required a point-wise bound of curvature tensors. As a coro...

The purpose of this survey is to give an overview of the results which characterize Riemannian manifolds with nonnegative or positive sectional, Ricci and scalar curvature, putting an emphasis on the differences between these increasingly strong conditions on curvature. All manifolds considered here are assumed to be complete. First we consider how nonnegative curvature is different from positi...