Related papers: Linear forms of a given Diophantine type
A vector variational principle is proved.
We formulate an exponential Diophantine equation, which is is some sense one order higher that Fermat's Last Theorem. We also give three examples of solutions to this exponential Diophantine equation and formulate a conjecture.
We provide infinitely many solutions of a Dirichlet problem on balls.
In this paper we study the spectrum of weak uniform Diophantine exponents of lattices and obtain its complete description in the two-dimensional case.
We develop a constructive process which determines all extreme points of the unit ball of the space of $m$--linear forms, $m\geq1.$ Our method provides a full characterization of the geometry of that space through finitely many elementary…
We prove an existence result for exact lagrangian cobordisms between closed legendrians.
We prove an analogue of the prime number theorem for finite fields.
We give a stack-theoretic proof for some results on families of hyperelliptic curves.
We prove that the construction of our previous paper math.QA/0103190 yields an invariant of tangle cobordisms.
We prove some theorems which give sufficient conditions for the existence of prime numbers among the terms of a sequence which has pairwise relatively prime terms.
We prove that two chains of linear mappings are topologically isomorphic if and only if they are linearly isomorphic.
We show that the theorem of the three perpendiculars holds in any n-dimensional space form.
We prove a stability theorem for families of holomorphically-parallelizable manifolds in the category of Hermitian manifolds.
We show that a finite number of commuting diffeomorphisms with simultaneously Diophantine rotation numbers are smoothly conjugated to roations.
In this paper one shows if the number of natural solutions of a general linear equation is limited or not. Also, it is presented a method of solving the Diophantine equation $ax-by=c$ in the set of natural numbers, and an example of solving…
We establish a general Liouville type theorem for conformally invariant fully nonlinear equations.
We prove various characterizations of the period torsor of abelian varieties. This is the submitted version.
We demonstrate how connections between graph theory and Diophantine approximation can be used in conjunction to give simple and accessible proofs of seemingly difficult results in both subjects.
We derive a Liouville type result for special Lagrangian equations with certain "convexity" and restricted linear growth assumptions on the solutions.
The paper is mostly a survey on recent results in Diophantine approximation, with emphasis on properties of exponents measuring various notions of Diophantine <approximation.