Related papers: A higher-dimensional version of F\'ary's theorem

We extend the fundamental normality test due to Carath\'eodory in the sense of shared functions.

In this paper, we prove a generalization of the Schmidt's subspace theorem for polynomials of higher degree in subgeneral position with respect to a projective variety over a number field. Our result improves and generalizes the previous…

We discuss some variants of cone theorem for movable curves in any codimensions.

In this paper, we state and prove a generalization of \'Ciri\'c fixed point theorems in metric space by using a new generalized quasi-contractive map. These theorems extend other well known fundamental metrical fixed point theorems in the…

Three generalizations of the well-known Ceva's Theorem are given in this paper and some applications.

We consider the immediate consequence of an arguable addition to the standard Deduction Theorems of first order theories.

A vector variational principle is proved.

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 $m$.

In this article we prove a multidimensional version of the Nazarov lemma. The proof is based on an appropriate generalisation of the regularised system of intervals introduced by Havin, Nazarov and Mashreghi to several dimensions.

We give a purely combinatorial proof for the infinitary van der Waerden's theorem.

We generalize certain arguments in Zariski's irregularity theorem on cyclic multiple planes.

An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…

We prove a generalization of the topological Tverberg theorem. One special instance of our general theorem is the following: Let $\Delta$ denote the 8-dimensional simplex viewed as an abstract simplicial complex, and suppose that its…

Our main theorem is an extension of the well-known Mizoguchi-Takahaashi's fixed point theorem [N. Mizogochi and W. Takahashi, Fixed point theorems for multi-valued mappings on complete metric space, {\it J. Math. Anal. Appl.} 141 (1989)…

Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.

The paper is devoted to generalization of well-known Michael's Selection theorem on the case of extension dimension.

We generalize Pappus chain theorem and give an analogue to this theorem.

We prove an analytic Bertini theorem, generalizing a previous result of Fujino and Matsumura.

A category which generalises to higher dimensions many of the features of the Temperley-Lieb category is introduced.

We prove two conjectures posed in 2016 concerning a generalization of the Sawayama-Th\'ebault Theorem and the Sawayama Lemma. We show that this generalized statement can be viewed in Laguerre geometry, which provides a natural framework for…