Related papers: Some remarks about Cauchy integrals
We give an up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds. We also mention some of their applications to time-dependent mechanics.
We lay foundations of the subject in the title, on which we build in another paper devoted to isometries in spaces of K\"ahler metrics.
Some aspects of the multidimensional soliton geometry are considered.
We show that Euclidean geometry in suitably high dimension can be expressed as a theory of orthogonality of subspaces with fixed dimensions and fixed dimension of their meet.
There are many papers studying properties of point sets in the Euclidean space $\mathbb{E}^m$ or on integer grids $\mathbb{Z}^m$, with pairwise integral or rational distances. In this article we consider the distances or coordinates of the…
In this paper, we systematically investigate the geometry and topology of manifolds with integral radial curvature bounds, and obtain many interesting and important conclusions.
Some geometric structures with associated Riemannian metrics have been considered in the book.
An exposition of the basic geometry of twistor integrals, intended for mathematicians.
The setting of metric spaces is very natural for numerous questions concerning manifolds, norms, and fractal sets, and a few of the main ingredients are surveyed here.
A common theme in mathematics is the evaluation of Gauss integrals. This, coupled with the fact that they are used in different branches of science, makes the topic always actual and interesting. In these notes we shall analyze a particular…
Various aspects of Supersymmetry in 1-dimensional systems are analyzed.
This article describes a natural piecewise Euclidean bi-simplicial cell structure for the space of $n$-element multisets in a fixed Euclidean rectangle. In particular, we highlight some connections with spaces of complex polynomials and…
The work consists of solutions of metric problems for convex and finite subsets of geodesic spaces.
Mass partition problems describe the partitions we can induce on a family of measures or finite sets of points in Euclidean spaces by dividing the ambient space into pieces. In this survey we describe recent progress in the area in addition…
We consider Cauchy type integrals $I(t)={1\over 2\pi i}\int_{\gamma} {g(z)dz\over z-t}$ with $g(z)$ an algebraic function. The main goal is to give constructive (at least, in principle) conditions for $I(t)$ to be an algebraic function, a…
This article is devoted to the study of classical and new results concerning equidistant sets, both from the topological and metric point of view. We start with a review of the most interesting known facts about these sets in the euclidean…
I consider compact metric spaces which admit intrinsic isometries to Euclidean d-space. The main result roughly states that the class of these spaces coincides with class of inverse limits of Euclidean d-polyhedra.
We study some basic properties and examples of Hermitian metrics on complex manifolds whose traces of the curvature of the Chern connection are proportional to the metric itself.
In this work we study the intrinsic geometry of the space of Kahler metrics under various Riemannian metrics. The first part is on the Dirichlet metric. We motivate its study, we compute its curvature, and we make links with the Calabi…
We provide an introduction to the old-standing problem of isometric immersions. We combine a historical account of its multifaceted advances, which have fascinated geometers and analysts alike, with some of the applications in the…