RIEMANNIAN GEOMETRY OF HARTOGS DOMAINS

Lineally convex Hartogs domains

We study lineally convex domains of a special type, viz. Hartogs domains, and prove that such sets can be characterized by local conditions if they are smoothly bounded.

A Geometry Preserving Kernel over Riemannian Manifolds

Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...

Riemannian geometry

Zeroes of the Bergman kernel of Hartogs domains

We exhibit a class of bounded, strongly convex Hartogs domains with realanalytic boundary which are not Lu Qi-Keng, i.e. whose Bergman kernel function has a zero.

Discrete Riemannian Geometry

Within a framework of noncommutative geometry, we develop an analogue of (pseudo) Riemannian geometry on nite and discrete sets. On a nite set, there is a counterpart of the continuum metric tensor with a simple geometric interpretation. The latter is based on a correspondence between rst order di erential calculi and digraphs (the vertices of the latter are given by the elements of the nite se...