Related papers: On Riemann's mapping theorem
We prove the existence of stationary discs in the ball for small almost complex deformations of the standard structure. We define a local analogue of the Riemann map and establish its main properties. These constructions are applied to…
In this paper we prove that every Riemannian metric on a locally conformally flat manifold with umbilic boundary can be conformally deformed to a scalar flat metric having constant mean curvature. This result can be seen as a generalization…
In the paper, we give a Schur-Toponogov theorem in Riemannian geometry, which not only generalizes Schur's and Toponogov's theorem but also indicates their relation. Inspired by its proof, we also supply a new proof of Toponogov's theorem…
We introduce an analog of the Kobayashi-Royden metric on a Riemannian manifold and study its basic properties.
We established a fixed-point theorem for mapping satisfying a general contractive inequality of integral type depended an another function. This theorem substantially extend the theorem due to Branciari (2003) and Rhoades (2003)
In the article a technique of the usage of $f$-continuous functions (on mappings) and their families is developed. A proof of the Urysohn's Lemma for mappings is presented and a variant of the Brouwer-Tietze-Urysohn Extension Theorem for…
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.
We give a short proof of Waldhausen's homeomorphism theorem for orientable Haken 3-manifolds.
Any three-dimensional Riemannian metric can be locally obtained by deforming a constant curvature metric along one direction. The general interest of this result, both in geometry and physics, and related open problems are stressed.
We consider a new type of mappings in metric spaces which can be characterized as mappings contracting perimeters of triangles. It is shown that such mappings are continuous. The fixed-point theorem for such mappings is proved and the…
The Riemann Theorem states, that for any nontrivial connected and simply connected domain on the Riemann sphere there exists some its conformal bijection to the exterior of the unit disk. In this paper we find an explicit form of this map…
In this paper we prove some new fixed point theorems for multivalued mappings on orbitally complete uniform spaces.
In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.
We provide a new formulation and proof of the triangle altitudes theorem in hyperbolic plane geometry, together with an easily computed discriminant to distinguish between different basic configurations of the altitudes of such a triangle.
The necessary and sufficient conditions for a three-dimensional Riemannian metric to admit a group of isometries of dimension $r$ acting on s-dimensional orbits are obtained. These conditions are Intrinsic, Deductive, Explicit and…
We give a new elementary proof of the parallelizability of closed orientable 3-manifolds. We use as the main tool the fact that any such manifold admits a Heegaard splitting.
In this paper, we prove a generalization of Geraghty's fixed point theorem for multi--valued mappings.
In this article we prove a theorem that will generalize the concurrence theorems that are leading to the Franke's point, Kariya's point, and to other remarkable points from the triangle geometry.
We prove a far-reaching generalization of Rickman's Picard theorem for a surprisingly large class of mappings, based on the recently developed theory of quasiregular values. Our results are new even in the planar case.
This paper presents an alternative approach to simplify the proofs of some important results related to polynomial mappings in Computational Algebraic Geometry such as Polynomial Implicitization, Image Closure and some properties of the…