Related papers: Multiplicity One Theorems, S-Version

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

In this paper we prove the multiplicity of solutions for a class of quasilinear problems in $ \mathbb{R}^{N} $ involving variable exponents. The main tool used is in the proof are the direct methods, Ekeland's variational principle and some…

We prove a new result on multiple summing operators and among other applications, we provide a new extension of Littlewood's $4/3$ inequality to $m$-linear forms.

We give a new elementary proof of existence and uniqueness of a solution to the Sylvester equation $AX-XB=Y$

In this paper, we first establish a K-theory version of the equivariant family index theorem for a circle action, then use it to prove several rigidity and vanishing theorems on the equivariant K-theory level.

We present a relative form of the Toponogov comparison theorem.

S.P.Novikov developed an analog of the Morse theory for closed 1-forms. In this paper I suggest an analog of the Lusternik - Schnirelman theory for closed 1-forms.

We show that a conceptually simple covering technique has surprisingly rich applications to density theorems and conjectures on patterns in sets involving set differences. These applications fall into three categories: (i) analogues of…

Based on the theory of invariant sets of descending flow, we give a new proof of the existence of three nontrivial solutions and some remarks on it.

An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…

In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.

The paper contains an alternative proof of M. Kontsevich Formality Theorem.

We discuss some aspects of the theory of subelliptic estimates.

In the paper we present some new inversion formulas and two new formulas for Stirling numbers.

We prove an explicit degree formula for certain unitary Deligne-Lusztig varieties. Combining with an alternative degree formula in terms of Schubert calculus, we deduce several algebraic combinatorial identities which may be of independent…

We formulate some conjectures about the K-theory of symplectic manifolds and their Fukaya categories, and prove some of them in very special cases.

For a class of quasilinear elliptic equations involving the p-Laplace operator, we develop an abstract critical point theory in the presence of sub-supersolutions. Our approach is based upon the proof of the invariance under the gradient…

In this note we give a detailed proof of certain results on geometry of numbers in the $S$-adic case. These results are well-known to experts, so the aim here is to provide a convenient reference for the people who need to use them.

We prove a density version of the Carlson--Simpson Theorem. Specifically we show the following. For every integer $k\geq 2$ and every set $A$ of words over $k$ satisfying \[\limsup_{n\to\infty} \frac{|A\cap [k]^n|}{k^n}>0\] there exist a…

This is an example on the cohomology of threefolds.