Related papers: Schottky's theorem in $\mathbb{C}^n$

The aim of this paper is to give a proof of improving of Zalcman's lemma.

The aim of this paper is to give some applications of Zalcman's Rescalling Lemma.

The aim of this paper is twofold. The first is to give a quantitative version of Schmidt's subspace theorem for arbitrary families of higher degree polynomials. The second is to give a generalization of the subspace theorem for arbitrary…

In this paper we go on to discuss about Stanley's theorem in Integer partitions. We give two different versions for the proof of the generalization of Stanley's theorem illustrating different techniques that may be applied to profitably…

It is known that Plotkin's reduction theorem is very important for his theory of universal algebraic geometry [arXiv:math. GM/0210187], [arXiv:math. GM/0210194]. It turns out that this theorem can be generalized to arbitrary categories…

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

Many versions of the Stokes theorem are known. More advanced of them require complicated mathematical machinery to be formulated which discourages the users. Our theorem is sufficiently simple to suit the handbooks and yet it is pretty…

In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].

Based on various strategies, we obtain several simple proofs of the celebrated Sharkovsky cycle coexistence theorem.

Chmieli\'{n}ski has proved in the paper [4] the superstability of the generalized orthogonality equation $|< f(x), f(y) >| = |< x, y >|$. In this paper, we will extend the result of Chmieli\'{n}ski by proving a theorem: Let $D_{n}$ be a…

We prove a variant of the standard Whitney extension theorem for $\mathcal C^m(\mathbb R^n)$, in which the norm of the extension operator has polynomial growth in $n$ for fixed $m$.

The aim of this note is to show that the "usual" proof of the Maschke Theorem in the case of a real and complex field can not be generalized at least to the case of a field of rational functions on a non-singular curve.

We prove a generic Torelli theorem for Jacobian elliptic surfaces, provided that the geometric genus is large compared to the irregularity. The result is effective to the extent that defining equations for the base curve are recovered from…

In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.

This article used Bloch function to derive Schottky inequality, obtained its generalization by using elliptic integral deviation function and demonstrated its applications.

The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].

We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.

The aim of this article is to give a new proof of Cohen-Gabber theorem in the equal characteristic $p>0$ case.

We prove an approximation theorem on a class of domains in $\mathbb{C}^n$ on which the $\overline{\partial}$-problem is solvable in $L^{\infty}$. Furthermore, as a corollary, we obtain a version of the Axler-\v{C}u\v{c}kovi\'c-Rao Theorem…