Related papers: On classical uniformization theorems for higher di…

We prove the Bers' density conjecture for singly degenerate Kleinian surfaces groups without parabolics.

At the end of 1960-ths Yu.S.Ilyashenko stated the problem: is it true that for any one-dimensional holomorphic foliation with singularities on a Stein manifold leaves intersecting a transversal disc can be uniformized so that the…

In this paper, we generalise the first Klein-Maskit combination theorem to discrete groups of M\"{o}bius transformations in higher dimensions. As a simple application of the main theorem, some examples will be constructed.

We show that uniqueness results of the kind those obtained for KdV and Schr\"odinger equations ([7], [28]), are not valid for the dispersion generalized-Benjamin-Ono equation in the weighted Sobolev spaces $$H^s(\R)\cap L^2(x^{2r}dx),$$ for…

We prove a generalization of a result of Peres and Schlag on the dimensions of certain exceptional sets of projections and then apply it to a geometric problem.

In this paper we study birational Kleinian groups, i.e.\ groups of birational transformations of complex projective varieties acting in a free, properly discontinuous and cocompact way on an open set of the variety with respect to the usual…

We prove a generalization of Bers' simultaneous uniformization theorem in the world of algebraic correspondences. More precisely, we construct algebraic correspondences that simultaneously uniformize a pair of non-homeomorphic genus zero…

Unlike the classical Brauer group of a field, the Brauer-Grothendieck group of a singular scheme need not be torsion. We show that there exist integral normal projective surfaces over a large field of positive characteristic with…

Classical Kleinian groups are discrete subgroups of $PSL(2,\C)$ acting on the complex projective line $\P^1$, which actually coincides with the Riemann sphere, with non-empty region of discontinuity. These can also be regarded as the…

After a historical discussion of classical uniformisation results for Riemann surfaces, of problems appearing in higher dimensions, and of uniformisation results for projective manifolds with trivial or ample canonical bundle, we introduce…

We consider the space of ordered pairs of distinct $\mathbb{C}P^1$-structures on Riemann surfaces (of any orientations) which have identical holonomy, so that the quasi-Fuchsian space is identified with a connected component of this space.…

By Koebe's retrosection theorem, every closed Riemann surface of genus $g \geq 2$ is uniformized by a Schottky group. Marden observed that there are Schottky groups that are not classical ones, that is, they cannot be defined by a suitable…

Let G be a smooth algebraic group acting on a variety X. Let F and E be coherent sheaves on X. We show that if all the higher Tor sheaves of F against G-orbits vanish, then for generic g in G, the sheaf Tor^X_j(gF, E) vanishes for all j >0.…

In this article, we revisit Weibel's conjecture for twisted $K$-theory. We also examine the vanishing of twisted negative $K$-groups for Pr\"{u}fer domains. Furthermore, we observe that the homotopy invariance of twisted $K$-theory holds…

We define united KK-theory for real C*-algebras A and B such that A is separable and B is sigma-unital, extending united K-theory in the sense that KK\crt(\R, B) = K\crt(B). United KK-theory contains real, complex, and self-conjugate…

Current quantum theories of an elementary free particle assume unitary space inversion and anti-unitary time reversal operators. In so doing robust classes of possible theories are discarded. The present work shows that consistent theories…

In this paper, we use the KK-theory of Kasparov to prove exactness of sequences relating the K-theory of a real C^*-algebra and of its complexification (generalizing results of Boersema). We use this to relate the real version of the…

Let $G$ be a connected reductive group defined over a non archimedean local field $k$. A theorem of Bernstein states that for any compact open subgroup $K$ of $G(k)$, there are, up to unramified twists, only finitely many $K$-spherical…

In this paper we parametrize the Teichm\"uller spaces of constructible Koebe groups, that is Kleinian group that arise as covering of $2-$orbifolds determined by certain normal subgroups of their fundamental groups. We also study the…

Let $X$ be a general complex projective hypersurface in $\mathbb{P}^{n+1}$ of degree $d>1$. A point $P$ not in $X$ is called uniform if the monodromy group of the projection of $X$ from $P$ is isomorphic to the symmetric group. We prove…