Related papers: Universal Curves in the Center Problem for Abel Di…

We consider the rational map $F$ defined by the quotient of products of lines in general position and we study the monodromy problem and tangential center-focus problem for the fibration associated with $F$. Thus, we study the submodule of…

The ancient unsolved problem of congruent numbers has been reduced to one of the major questions of contemporary arithmetic: the finiteness of the number of curves over $\bf Q$ which become isomorphic at every place to a given curve. We…

We study analytical and computational aspects for Dirichlet problem on the unit ball $B$: $|x|<1$ in $R^n$, modeled on the equation \[ \Delta u +\lambda \left(u^p+u^q \right)=0, \;\; \mbox{in $B$}, \;\; u=0 \s \mbox{on $\partial B$}, \]…

Let $C$ be an affine curve over an algebraically closed field $k$ of characteristic $p>0$. Given an embedding problem $(\beta:\Gamma\longrightarrow G, \alpha: \pi^{et}_1(C)\longrightarrow G)$ for $\pi_1^{et}(C)$ where $\beta$ is a…

We show that the canonical central extension of the group of sections of a Lie group bundle over a compact manifold, constructed in [NW09], is universal. In doing so, we prove universality of the corresponding central extension of Lie…

The first part of the paper centers in the study of embeddability between partially commutative groups. In [KK], for a finite simplicial graph $\Gamma$, the authors introduce an infinite, locally infinite graph $\Gamma^e$, called the…

A classical solution is called universal if the quantum correction is a multiple of the metric. Universal solutions consequently play an important role in the quantum theory. We show that in a spacetime which is universal all of the scalar…

We give the explicit equations for a P^3 x P^3 embedding of the Jacobian of a curve of genus 2, which gives a natural analog for abelian surfaces of the Edwards curve model of elliptic curves. This gives a much more succinct description of…

For regular one-dimensional variational problems, Ball and Nadirashvilli introduced the notion of the universal singular set of a Lagrangian L and established its topological negligibility. This set is defined to be the set of all points in…

Let $\Gamma$ be a bounded Jordan curve and $\Omega_i,\Omega_e$ its two complementary components. For $s\in(0,1)$ we define $\mathcal{H}^s(\Gamma)$ as the set of functions $f:\Gamma\to \mathbb C$ having harmonic extension $u$ in…

In this paper we show that the invariant Cantor set of period doubling type of any infinitely renormalizable area-preserving map in the universality class of the Eckmann-Koch-Wittwer renormalization fixed point is always contained in a…

J.Bella\"iche and M.Dimitrov have shown that the $p$-adic eigencurve is smooth but not etale over the weight space at $p$-regular theta series attached to a character of a real quadratic field $F$ in which $p$ splits. We proof in this paper…

Weighted discrete Hilbert transforms $(a_n)_n \mapsto \big(\sum_n a_n v_n/(\lambda_j-\gamma_n)\big)_j$ from $\ell^2_v$ to $\ell^2_w$ are considered, where $\Gamma=(\gamma_n)$ and $\Lambda=(\lambda_j)$ are disjoint sequences of points in the…

We compute Seidel's mirror map for abelian varieties by constructing the homogeneous coordinate rings from the Fukaya category of the symplectic mirrors. The computations are feasible as only linear holomorphic disks contribute to the…

We show that for a certain family of integrable reversible transformations, the curves of periodic points of a general transformation cross the level curves of its integrals. This leads to the divergence of the normal form for a general…

In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum…

We approach the problem of uniformization of general Riemann surfaces through consideration of the curvature equation, and in particular the problem of constructing Poincar\'e metrics (i.e., complete metrics of constant negative curvature)…

Let $X(\Gamma)$ be the space of all finite Borel measure $\mu$ in $\mathbb R^2$ which is supported on the curve $\Gamma$ and absolutely continuous with respect to the arc length of $\Gamma$. For $\Lambda\subset\mathbb R^2,$ the pair…

We complete the problem of finding the universal central extension in the category of Leibniz superalgebras of $\mathfrak{sl}(m, n, D)$ when $m+n \geq 3$ and $D$ is a superdialgebra, solving in particular the problem when $D$ is an…

We solve the local equivalence problem for second order (smooth or analytic) ordinary differential equations. We do so by presenting a {\em complete convergent normal form} for this class of ODEs. The normal form is optimal in the sense…