Related papers: A higher-dimensional version of F\'ary's theorem
In this paper we give a new proof of Riemann's well known mapping theorem. The suggested method permits to prove an analog of that theorem for the three dimensional case.
A generalization of the law of total covariance is presented and proved.
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 generalization of Tur\'{a}n's theorem proposed by Balogh and Lidick\'{y}.
We generalize Romanoff's theorem. Also, we obtain a result on sums related to Euler's totient function.
By combining Tur\'an's proof of Fabry's gap theorem with a gap theorem of P. Sz\"usz we obtain a gap theorem which is more general then both these theorems.
We prove a variation of Gronwall's lemma.
We establish cohomological and extension dimension versions of the Hurewicz dimension-raising theorem
We present a new proof of the Joints Theorem without taking derivatives. Then we generalize the proof to prove the Multijoints Conjecture and Carbery's generalization. All results are in any dimension over an arbitrary field.
In this paper, we give a refinement of a theorem by Franks, which answers two questions raised by Kang.
This paper presents a proof of Gallai's Theorem, adapted from A. Soifer's presentation in The Mathematical Coloring Book of E. Witt's 1952 proof of Gallai's Theorem.
We prove the Aharoni Berger Conjecture
In this note a far extension of the Banach fixed point theorem is proved.
A key ingredient in the Taylor-Wiles proof of Fermat last theorem is the classical Ihara's lemma which is used to rise the modularity property between some congruent galoisian representations. In their work on Sato-Tate,…
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
We give a natural proof of the Ado theorem.
We provide a new proof of Vivinai's Theorem using what George Polya calls a 'leading particular case.' Our proof highlights the role of generalization in mathematics.
In this article we prove a generalization of the Beurling--Malliavin Majorant Theorem. In more detail, we establish a new sufficient condition for a function to be a Beurling--Malliavin Majorant. Our result is strictly more general than…
We show that a problem by Yau can not be true in general. The counterexamples are constructed based on the recent work of Wu and Zheng.
We prove a new theorem on additive Levy processes and show that this theorem implies several proved theorems and a hard conjectured theorem.