Related papers: Towards a Classification of Homogeneous Tube Domai…

We determine all affinely homogeneous models for surfaces $S^2 \subset \mathbb{R}^4$, including the simply transitive models. We employ an improved power series method of equivalence, which captures invariants at the origin, creates…

We first show that for a bounded pseudoconvex domain with a manifold quotient of finite-volume in the sense of Kahler-Einstein measure, the identity component of the automorphism group of this domain is semi-simple without compact factors.…

The Levi geometry at weakly pseudoconvex boundary points of domains in C^n, n \geq 3, is sufficiently complicated that there are no universal model domains with which to compare a general domain. Good models may be constructed by bumping…

We consider a problem whether a given Lie group can be realized as the group of all biholomorphic automorphisms of a bounded domain in ${\mathbb C}^n$. In an earlier paper of 1990, we proved the result for connected linear Lie groups. In…

Fels-Kaup (Acta Mathematica 2008) classified homogeneous $\mathfrak{C}_{2,1}$ hypersurfaces $M^5 \subset \mathbb{C}^3$ and discovered that they are all biholomorphic to tubes $S^2 \times i \mathbb{R}^3$ over some affinely homogeneous…

In this paper the singular hypersurfaces in $\mathbb{C}\mathrm{P}^4$ of degree $d$ with an isolated singularity are studied. If the singularity is of type $A_{2k+1}$, under the condition $d<(k+5)/2$, a classification of such hypersurfaces…

Let X=G/H be the quotient of a connected reductive algebraic C-group G defined over the field of complex numbers C by a finite subgroup H. We describe the topological fundamental group of the homogeneous space X, which is nonabelian when H…

We consider Levi non-degenerate tube hypersurfaces in $\CC^{n+1}$ that are $(k,n-k)$-spherical, i.e. locally CR-equivalent to the hyperquadric with Levi form of signature $(k,n-k)$, with $n\le 2k$. We show that the number of affine…

We give a geometric model for a tube category in terms of homotopy classes of oriented arcs in an annulus with marked points on its boundary. In particular, we interpret the dimensions of extension groups of degree 1 between indecomposable…

We study the semicontinuity of automorphism groups for perturbations of domains in complex space or in complex manifolds. We provide a new approach to the study of such results for domains having minimal boundary smoothness. The emphasis in…

In this paper we study the geometry and the topology of unbounded domains in the Hyperbolic Space $\mathbb{H} ^n$ supporting a bounded positive solution to an overdetermined elliptic problem. Under suitable conditions on the elliptic…

Locally homogeneous CR-manifolds in dimension 3 were classified, up to local CR-equivalence, by E.Cartan. We classify, up to local CR-equivalence, all locally homogeneous CR-manifolds in dimension 4. The classification theorem enables us…

We give a description (direct formulas) of all complex geodesics in a convex tube domain in $\CC^n$ containing no complex affine lines, expressed in terms of geometric properties of the domain. We next apply that result to give formulas (a…

We prove that the homology of the mapping class groups of non-orientable surfaces stabilizes with the genus of the surface. Combining our result with recent work of Madsen and Weiss, we obtain that the classifying space of the stable…

We construct the first examples of non-smoothable self-homeomorphisms of smooth $4$-manifolds with boundary that fix the boundary and act trivially on homology. As a corollary, we construct self-diffeomorphisms of $4$-manifolds with…

Solenoids are inverse limit spaces over regular covering maps of closed manifolds. M.C. McCord has shown that solenoids are topologically homogeneous and that they are principal bundles with a profinite structure group. We show that if a…

Let (L;C) be the (up to isomorphism unique) countable homogeneous structure carrying a binary branching C-relation. We study the reducts of (L;C), i.e., the structures with domain L that are first-order definable in (L;C). We show that up…

We prove that the space of dominant/non-constant holomorphic mappings from a product of hyperbolic Riemann surfaces of finite type into certain hyperbolic manifolds with universal cover a bounded domain is a finite set.

We prove that there exist infinitely many embedded tori with a common geometric dual in $T^4\#(S^2\times S^2)$ that are homotopic, diffeomorphic, but not isotopic to each other, even after arbitrary many external stabilizations. These…

In this work, we give a survey on non characteristic domains of Heisenberg groups. We prove that bounded domains which are diffeomorphic to the solid torus having the center of the group as rotation axis, are non characteristic. Then, we…