Related papers: The Heyde Theorem on a-adic Solenoids
We prove a combination theorem for PD(n)-pairs.
We prove an analogue of Clifford's inequality for tropical curves. Next we focus on the hyperelliptic case and we characterize divisors attaining equality. Finally we speculate whether inequality in tropical Clifford's Theorem does imply…
We show that any proper Lie groupoid admits a compatible (real) analytic structure.
We give a short proof of a strengthening of the Maximal Ergodic Theorem which also immediately yields the Pointwise Ergodic Theorem.
Torelli's theorem is proven by the study of the convolution product of the intersection cohomology sheaf of the thetadivisor.
We extend the famous Erd\H{o}s-Szekeres theorem to $k$-flats in ${\mathbb{R}^d}$
We prove a Chevalley restriction theorem and its double analogue for the cyclic quiver.
We considered real, p-adic and adelic noncommutative scalar solitons and obtained some new results.
We prove an Erd\H{o}s--Tur\'an type inequality for compact Lie groups, from which we deduce an effective version of Deligne's equidistribution theorem.
We establish analogues of Hardy's theorem for Gabor transform on locally compact abelian groups, Euclidean motion group and several general classes of nilpotent Lie groups which include Heisenberg groups, thread-like nilpotent Lie groups,…
We prove a duality theorem for quantum groupoid (weak Hopf algebra) actions that extends the well-known result for usual Hopf algebras.
This is the second paper of a series. It extends the results of the first paper from number fields to finitely generated fields, based on the recent theory of adelic line bundles of the same authors. We prove an arithmetic Hodge index…
In this note, we will consider an arithmetic analogue of Bogomolov unstability theorem.
We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.
We prove an interpolation theorem for bounded free holomorphic functions.
We give a short and relatively elementary proof of the Hilton-Milner Theorem.
We introduce singular subalgebroids of an integrable Lie algebroid, extending the notion of Lie subalgebroid by dropping the constant rank requirement. We lay the bases of a Lie theory for singular subalgebroids: we construct the associated…
In this article, we prove a theorem comparing the dihedral angles of simplices in the hyperbolic, spherical and Euclidean geometries.
This is an overview article on Lie algebroids, and their role as the infinitesimal counterparts of Lie groupoids.
We study the Hadwiger-Alesker finiteness theorem from the standpoint of Lie theory and announce a generalization.