Related papers: An overtwisted convex hypersurface in higher dimen…

We obtain several results for (iterated) planar contact manifolds in higher dimensions: (1) Iterated planar contact manifolds are not weakly symplectically semi-fillable. This generalizes a 3-dimensional result of Etnyre to a…

We give an alternative proof of a theorem of Honda-Kazez-Mati\'c that every non-right-veering open book supports an overtwisted contact structure. We also study two types of examples that show how overtwisted discs are embedded relative to…

Having in mind the well known model of Euclidean convex hypersurfaces [4], [5], and the ideas in [1] many authors defined and investigate convex hypersurfaces of a Riemannian manifold. As it was proved by the first author in [7], there…

We develop a method for preserving pseudoholomorphic curves in contact 3-manifolds under surgery along transverse links. This makes use of a geometrically natural boundary value problem for holomorphic curves in a 3-manifold with stable…

We prove every oriented compact cyclic $3$-orbifold has a contact structure. There is another proof in the web by Daniel Herr in his uploaded thesis which depends on open book decompositions, ours is independent of that. We define…

A projective hypersurface $X \subseteq \mathbb P^n$ has defect if $h^i(X) \neq h^i(\mathbb P^n)$ for some $i \in \{n, \dots, 2n-2\}$ in a suitable cohomology theory. This occurs for example when $X \subseteq \mathbb P^4$ is not $\mathbb…

We study pseudoholomorphic discs with boundaries attached to a real hypersurface in an almost complex manifold of dimension 2. We prove that if the hypersurface contains no discs, then they fill a one sided neighborhood of the hypersurface.

We show the existence of elements of infinite order in some homotopy groups of the contactomorphism group of overtwisted spheres. It follows in particular that the contactomorphism group of some high dimensional overtwisted spheres is not…

Consider a smooth manifold with a smooth metric which changes bilinear type from Riemann to Lorentz on a hypersurface $\Sigma$ with radical tangent to $\Sigma$. Two natural bilinear symmetric forms appear there, and we use it to analyze the…

We give an explicit verifiable characterization of weakly pseudoconvex but locally nonconvexifiable hypersurfaces of finite type in dimension two. It is expressed in terms of a generalized model, which captures local geometry of the…

We show that for a very general and natural class of curvature functions, the problem of finding a complete strictly convex hypersurface satisfying f({\kappa}) = {\sigma} over (0,1) with a prescribed asymptotic boundary {\Gamma} at infinity…

We use convex decomposition theory to (1) reprove the existence of a universally tight contact structure on every irreducible 3-manifold with nonempty boundary, and (2) prove that every toroidal 3-manifold carries infinitely many…

We establish the Hodge conjecture for some subvarieties of a class of toric varieties. First we study quasi-smooth intersections in a projective simplicial toric variety, which is a suitable notion to generalize smooth complete intersection…

We exhibit a closed hyperbolic 3-manifold which satisfies a very strong form of Thurston's Virtual Fibration Conjecture. In particular, this manifold has finite covers which fiber over the circle in arbitrarily many ways. More precisely, it…

The set N of all null geodesics of a globally hyperbolic (d+1)-dimensional spacetime (M,g) is naturally a smooth (2d-1)-dimensional contact manifold. The sky of an event is the subset of N defined by all null geodesics through that event,…

We compute the homotopy type of the space of embeddings of convex disks with Legendrian boundary into a tight contact $3$-manifold, whenever the sum of the absolute value of the rotation number of the boundary with the Thurston-Bennequin…

Let ($M$, $\Omega$) be a smooth symplectic manifold and $f:M\rightarrow M$ be a symplectic diffeomorphism of class $C^l$ ($l\geq 3$). Let $N$ be a compact submanifold of $M$ which is boundaryless and normally hyperbolic for $f$. We suppose…

In this work we present a study on the characterization of ordered and disordered hyperuniform point distributions on spherical surfaces. In spite of the extensive literature on disordered hyperuniform systems in Euclidean geometries, to…

We analyze the critical connectivity of systems of penetrable $d$-dimensional spheres having size distributions in terms of weighed random geometrical graphs, in which vertex coordinates correspond to random positions of the sphere centers…

We consider a partially overdetermined problem in a sector-like domain $\Omega$ in a cone $\Sigma$ in $\mathbb{R}^N$, $N\geq 2$, and prove a rigidity result of Serrin type by showing that the existence of a solution implies that $\Omega$ is…