Let f : X −→ S be a smooth projective family and let (L, h) be a singular hermitian line bundle on X with semipositive curvature current. Let Ks := K(Xs, KXs +L | Xs, h | Xs)(s ∈ S) be the Bergman kernel of KXs +L | Xs with respect to h | Xs and let hB the singular hermitian metric on KX + L defined by hB |Xs := 1/Ks. We prove that hB has semipositive curvature. This is a generalization of the ...

Chronic graft versus host disease (GvHD) after allogeneic stem cell transplantation (SCT) may involve any organ system, but male genital involvement is rare. Peyronie's Disease (PD) is an acquired, localized fibrotic disorder of the tunica albuginea, which leads to penile deformity, pain, and eventually to erectile dysfunction. We report the case of a 52 year old African American male with Acut...

we prove that every r-quadratic metric of scalar flag curvature with a dimension greater than twois of constant flag curvature. then we show that generalized douglas-weyl metrics contain r-quadraticmetrics as a special case, but the class of r-quadratic metric is not closed under projective transformations

in this paper the general relatively isotropic l -curvature finsler metrics are studied. it isshown that on constant relatively landsberg spaces, the concepts of weakly landsbergian, landsbergianand generalized landsbergian metrics are equivalent. some necessary conditions for a relativelyisotropic l -curvature finsler metric to be a riemannian metric are also found.

One of the basic problems of Riemannian geometry is the classification of manifolds of positive sectional curvature. The known examples include the spherical space forms which carry constant curvature metrics and the rank 1 symmetric spaces whose canonical metrics have sectional curvatures at each point varying between 1 and 4. In 1951 H.E. Rauch [18] introduced the notion of curvature pinching...

Let M be a compact k-dimensional riemmanian manifold minimally immersed in the unit n-dimensional sphere S. It is easy to show that for any p ∈ S the boundary of the geodesic ball in S with radius π2 and center at p (in this case this boundary is an equator) must intercept the manifold M . When the codimension is 1, i.e. k = n − 1, it is known that the ricci curvature, is not greater than 1. We...

In this article, we will give a brief survey on some recent development concerning the understanding of the structure at infinity of a complete manifold whose spectrum has a positive lower bound. Throughout this paper, we denote M to be a complete n-dimensional manifold without boundary endowed with the metric ds. We assume that the Ricci curvature of M is bounded from below by some constant. R...

PURPOSE To describe longitudinal changes in corneal curvature (CC) and axial length (AL) over 14 years, and to explore the relationship between AL and CC, and the axial length/corneal radius (AL/CR) ratio. METHODS In total 469, 6 to <12-year-old, children were enrolled in COMET. Measurements of refractive error, CC (D), CR (mm), and ocular component dimensions including AL were gathered annua...

The conformal monogenic signal is a novel rotational invariant approach for analyzing i(ntrinsic)1D and i2D local features of twodimensional signals (e.g. images) without the use of any heuristics. It contains the monogenic signal as a special case for i1D signals and combines scale-space, phase, orientation, energy and isophote curvature in one unified algebraic framework. The conformal monoge...