The goal of this article is to present a survey of the recent theory of plurisubharmonic functions of quaternionic variables, and its applications to theory of valuations on convex sets and HKT-geometry (HyperKähler with Torsion). The exposition follows the articles [4], [5], [7] by the author and [8] by M. Verbitsky and the author.

Manifolds with special geometric structures play a prominent role in some branches of theoretical physics, such as string theory and supergravity. For instance, it is well known that supersymmetry requires target spaces to have certain special geometric properties. In many cases these requirements can be interpreted as restrictions on the holonomy group of the target space Riemannian metric. Ho...

A hypercomplex manifold is a manifold equipped with a triple of complex structures I, J,K satisfying the quaternionic relations. We define a quaternionic analogue of plurisubharmonic functions on hypercomplex manifolds, and interpret these functions geometrically as potentials of HKT (hyperkähler with torsion) metrics, and prove a quaternionic analogue of A.D. Aleksandrov and Chern-Levine-Niren...

The goal of this article is to present a survey of the recent theory of plurisubharmonic functions of quaternionic variables, and its applications to theory of valuations on convex sets and HKT-geometry (HyperKähler with Torsion). The exposition follows the articles [4], [5], [7] by the author and [8] by M. Verbitsky and the author.

BACKGROUND High affinity potassium transporters (HKTs) are located in the plasma membrane of the vessels and have significant influence on salt tolerance in some plants. They exclude Na(+) from the parenchyma cells to reduce Na(+) concentration. Despite many studies, the underlying regulatory mechanisms and the exact functions of HKTs within different genomic backgrounds are relatively unknown....

background and objectives: this research study was conducted to determine the correlation between the clinicopathologic features and the outcome of membranous nephropathy. materials and methods: data were retrospectively reviewed from all patients with a diagnosis of membranous nephropathy. demographic, initial laboratory, and clinical findings were collected and the biopsy specimens were revie...

Background and Objectives: This research study was conducted to determine the correlation between the clinicopathologic features and the outcome of membranous nephropathy. Materials and Methods: Data were retrospectively reviewed from all patients with a diagnosis of membranous nephropathy. Demographic, ...