Related papers: On Riemann's mapping theorem
We give an elementary and self-contained proof of the uniformization theorem for non-compact simply-connected Riemann surfaces.
The classical Three Gap Theorem asserts that for a natural number n and a real number p, there are at most three distinct distances between consecutive elements in the subset of [0,1) consisting of the reductions modulo 1 of the first n…
The aim of the present paper is to study the properties of Riemannian manifolds equipped with a projective semi-symmetric connection.
Recently we generalized Toponogov's comparison theorem to a complete Riemannian manifold with smooth convex boundary, where a geodesic triangle was replaced by an open (geodesic) triangle standing on the boundary of the manifold, and a…
In this note, we give an equivalent condition for a self-dual weight enumerator of genus three to satisfy the Riemann hypothesis. We also observe the truth and falsehood of the Riemann hypothesis for some families of invariant polynomials.
This note presents a new proof of the well-known Strichartz estimates for the Schr\"odinger equation in $2+1$ dimensions, building on ideas from our recent work \cite{MO}.
For the bi-orthogonal polynomials with the third degree polynomial potential functions, the 3 x 3 matrix Riemann-Hilbert problem is explicitly constructed. The developed approach admits an extension to the bi-orthogonal polynomials with…
We show that the Euler-MacLaurin formula for Riemann sums has an n-dimensional analogue in which intervals on the line get replaced by convex polytopes.
The subject of this paper is Beurling's celebrated extension of the Riemann mapping theorem \cite{Beu53}. Our point of departure is the observation that the only known proof of the Beurling-Riemann mapping theorem contains a number of gaps…
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.
We give geometric proofs for Grobman-Hartman theorem for diffeomorphisms and ODEs. Proofs use covering relations and cone conditions for maps and isolating segments and cone condition for ODEs. We prove also the H\"older condition for the…
This article contains the proof of a theorem on orthogonal-Pin duality that was cited without proof in a previous article in this journal.
We prove an orbifold Riemann--Roch formula for a polarized 3--fold (X,D). As an application, we construct new families of projective Calabi--Yau threefolds.
We studied rules of transformations of Christoffel symbols under third type almost geodesic mappings in this paper. From this research, we obtained some new invariants of these mappings. These invariants are analogies of Thomas projective…
We prove that polyharmonic maps of arbitrary order from complete nonparabolic Riemannian manifolds to arbitrary Riemannian manifolds must be harmonic if certain smallness and integrability conditions hold.
We prove a result on the structure of finite proper holomorphic mappings between complex manifolds that are products of hyperbolic Riemann surfaces. While an important special case of our result follows from the ideas developed by Remmert…
Following suggestions of T. H. Koornwinder, we give a new proof of Kummer's theorem involving Zeilberger's algorithm, the WZ method and asymptotic estimates. In the first section, we recall a classical proof given by L. J. Slater. The…
In terms of dilatations, it is proved a series of criteria for continuous and homeomorphic extension to the boundary of mappings with finite distortion between regular domains on the Riemann surfaces
It is well-known that a finite graph can be viewed, in many respects, as a discrete analogue of a Riemann surface. In this paper, we pursue this analogy further in the context of linear equivalence of divisors. In particular, we formulate…
We will give a new proof for the Gromov's theorem on almost flat manifolds, which is an inductive proof on dimension.