Related papers: Formes de Whitney et primitives relatives de forme…

We study weak approximation on rationally connected varieties under an assumption of strong approximation for a "simple" variety or under Schinzel's hypothesis. We also get some unconditional results.

We are to establish necessary conditions (of the primal and dual types) for the set of weak sharp minima of a nonconvex optimization problem on a Riemannian manifold. Here, we are to provide a generalization of some characterizations of…

For $g\geq 0$, a genus $g$ Kashiwara-Vergne associator, introduced by Alekseev-Kawazumi-Kuno-Naef as a solution to the generalised KV equations in relation to the formality problem of the Goldman-Turaev Lie bialgebra on an oriented surface…

We introduce weak oddness $\omega_{\textrm w}$, a new measure of uncolourability of cubic graphs, defined as the least number of odd components in an even factor. For every bridgeless cubic graph $G$, $\rho(G)\le\omega_{\textrm…

Let $G$ be a finite primitive permutation group on a set $\Omega$ with nontrivial point stabilizer $G_{\alpha}$. We say that $G$ is extremely primitive if $G_{\alpha}$ acts primitively on each of its orbits in $\Omega \setminus \{\alpha\}$.…

Given an algebraic difference equation of the form \[\sigma^n(y)=f\big(y, \sigma(y),\dots,\sigma^{n-1}(y)\big)\] where $f$ is a rational function over a field $k$ of characteristic zero on which $\sigma$ acts trivially, it is shown that if…

We show that there are precisely two, up to conjugation, anti-involutions sigma_{\pm} of the algebra of differential operators on the circle preserving the principal gradation. We classify the irreducible quasifinite highest weight…

We recall the construction of the Hodge character and we show, using a result due to F. Bittner, that these can be constructed using classical pure Hodge theory only, sideskipping Deligne's construction of functorial mixed Hodge structures…

We prove the analogue of Viehweg's hyperbolicity conjecture for Whitney equisingular families of projective varieties with Gorenstein rational singularities whose geometric generic fiber has a good minimal model. Namely, for such families…

The purpose of this paper is to address a manifold-based version of Whitney's extension problem: Given a compact set $E\subset\mathbb{R}^n$, how can we tell if there exists a $d$-dimensional, $C^m$-smooth manifold $\mathcal{M}\supset E$? We…

As is well-known, the Witten deformation of the De Rham complex computes the De Rham cohomology. In this paper we study the Witten deformation on a noncompact manifold and restrict it to differential forms which behave polynomially near…

Let $\Omega\subset \mathbb{R}^{n}$ be a bounded open set. Given $1\leq m_1,m_2\leq n-2$, we construct a homeomorphism $f :\Omega\to \Omega$ that is H\"older continuous, $f$ is the identity on $\partial \Omega$, the derivative $D f$ has rank…

We construct finite element approximations of the Levi-Civita connection and its curvature on triangulations of oriented two-dimensional manifolds. Our construction relies on the Regge finite elements, which are piecewise polynomial…

The conformal Willmore functional (which is conformal invariant in general Riemannian manifold $(M,g)$) is studied with a perturbative method: the Lyapunov-Schmidt reduction. Existence of critical points is shown in ambient manifolds…

Let $\Sigma$ be a complete Riemannian manifold of nonnegative Ricci curvature. We prove a Liouville-type theorem: every smooth solution $u$ to minimal hypersurface equation on $\Sigma$ is a constant provided $u$ has sublinear growth for its…

Let $A$ be an abelian variety defined over a number field $K$. We say that a point $P \in A(\overline{\mathbb{Q}})$ is primitive if there is no $Q \in A(\overline{\mathbb{Q}})$ defined on the field of definition of $P$ over $K$ such that…

We study primitive elements in the Ringel-Hall algebra H(A) of an algebra A over a finite field associated with a quiver with automorphism. When A is a tame hereditary algebra, we give a description of primitive elements in H(A) which…

In these notes we study the Dirichlet problem for critical points of a convex functional of the form \[ F(u)=\int_{\Omega}\phi\left( \left\vert \nabla u\right\vert \right) , \] where $\Omega$ is a bounded domain of a complete Riemannian…

We extend two well-known results on primitive ideals in enveloping algebras of semisimple Lie algebras, the `Irreducibility theorem' and `Duflo theorem', to much wider classes of algebras. Our general version of Irreducibility theorem says…

Let $G/\Gamma$ be the quotient of a semisimple Lie group by an arithmetic lattice. We show that for reductive subgroups $H$ of $G$ that is large enough, the orbits of $H$ on $G/\Gamma$ intersect nontrivially with a fixed compact set. As a…