Related papers: On Riemann's mapping theorem
In this paper we use a dynamical approach to prove some new divergence theorems on complete non-compact Riemannian manifolds.
An analog of Picard's little theorem for entire functions of matrices is proved.
A proposed solution to the Riemann Hypothesis
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.
We give a new simpler proof of a theorem of Jayne and Rogers.
In this article we show how holomorphic Riemannian geometry can be used to relate certain submanifolds in one pseudo-Riemannian space to submanifolds with corresponding geometric properties in other spaces. In order to do so, we shall first…
A useful result is that if a bounded complex-valued path is Riemann-integrable, then its modulus is also Riemann-integrable. The extension of this last result to bounded paths taking values in a normed space is affirmed, as being true, in…
In this paper, we introduce Clairaut warped product Riemannian maps. To study these kind of maps, first, we find the condition of geodesic of a regular curve. Then we obtain the conditions for a warped product Riemannian map to be Clairaut…
We provide a simple proof of Kamp's theorem.
We introduce the notion of Riemannian twistorial structure and we show that it provides new natural constructions of harmonic maps.
We prove a generalization of Kannan's fixed point theorem, based on a recent result of Vittorino Pata.
Under some natural hypotheses, we show that if a multilinear mapping belongs to some Banach multlinear ideal, then it can be approximated by multilinear mappings belonging to the same ideal whose Arens extensions simultaneously attain their…
This is a new version of our previous work. In this version, we fill a gap included in the original proof of Theorem 1.1 in our previous paper entitled "An iterative method for Kirchhoff type equations and its applications".
Our main aim in this paper is to introduce a general concept of multidimensional fixed point of a mapping in spaces with distance and establish various multidimensional fixed point results. This new concept simplifies the similar notion…
We will simplify the earlier proofs of Perelman's collapsing theorem of 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's semi-convex analysis of distance functions to construct the desired local…
The leading idea of the paper is to treat the theorem of Wigner with methods inspired by geometry. The exercise mentionned in the title has two functions: On the one hand it can serve as a pedagogical text in order to make the reader…
We comment on some apparently weak points in the novel strategies recently developed by various authors aiming at a proof of the Riemann hypothesis. After noting the existence of relevant previous papers where similar tools have been used,…
We introduce a notion of metric on a Lie groupoid, compatible with multiplication, and we study its properties. We show that many families of Lie groupoids admit such metrics, including the important class of proper Lie groupoids. The…
Beginning from the resolution of Dirichlet L function, using the inner product formula of infinite-dimensional vectors in the complex space, the author proved the world's baffling problem--Generalized Riemann hypothesis.
By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.