相关论文: Uniform 1-Cochains and Genuine Laminations

We show that every atoroidal endperiodic map of an infinite-type surface can be obtained from a depth one foliation in a fibered hyperbolic 3-manifold, reversing a well-known construction of Thurston. This can be done almost-transversely to…

This manuscript develops a geometric approach to ordinary cohomology of smooth manifolds, constructing a cochain complex model based on co-oriented smooth maps from manifolds with corners. Special attention is given to the pull-back product…

For every atoroidal iwip automorphism $\phi$ of $F_N$ (i.e. the analogue of a pseudo-Anosov mapping class) it is shown that the algebraic lamination dual to the forward limit tree $T_+(\phi)$ is obtained as "diagonal closure" of the support…

We prove existence and nonexistence results for annular type parametric surfaces with prescribed, almost constant mean curvature, characterized as normal graphs of compact portions of unduloids or nodoids in $\mathbb{R}^{3}$, and whose…

We establish analytic linearization of s-proper analytic groupoids around invariant submanifolds. We apply this result to show that any such groupoid admits a holomorphic extension.

We prove that compact 3-manifolds $M$ of constant curvature +1 with boundary a minimal surface are locally naturally parametrized by the conformal class of the boundary metric $\gamma$ in the Teichmuller space of $\partial M$, when…

Despite the invertible setting, Anosov endomorphisms may have infinitely many unstable directions. Here we prove, under transitivity assumption, that an Anosov endomorphism on a closed manifold $M,$ is either special (that is, every $x \in…

We show theoretically that essentially perfect elastostatic mechanical cloaking of a circular inclusion in a homogeneous surrounding medium can be achieved by means of a simple cloak comprising three concentric annuli, each formed of a…

This paper presents a novel implicit representation of solid models. With this representation, every solid model can be effectively presented by three layered depth-normal images (LDNIs) that are perpendicular to three orthogonal axes…

We study the Gram determinant and construct bases of hom spaces for the one-dimensional topological theory of decorated unoriented one-dimensional cobordisms, as recently defined by Khovanov, when the pair of generating functions is linear.

About a decade ago Thurston proved that a vast collection of 3-manifolds carry metrics of constant negative curvature. These manifolds are thus elements of {\em hyperbolic geometry}, as natural as Euclid's regular polyhedra. For a closed…

We study a notion of strict pseudoconvexity in the context of topologically (often unsmoothably) embedded 3-manifolds in complex surfaces. Topologically pseudoconvex (TPC) 3-manifolds behave similarly to their smooth analogues, cutting out…

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…

The principle "ambient cohomology of a Kaehler manifold annihilates obstructions" has been known and exploited since pioneering work of Kodaira. This paper extends and unifies many known results in two contexts, abstract deformations of…

Transversal structures (also known as regular edge labelings) are combinatorial structures defined over 4-connected plane triangulations with quadrangular outer-face. They have been intensively studied and used for many applications…

Finite-order invariants of knots in arbitrary 3-manifolds (including non-orientable ones) are constructed and studied by methods of the topology of discriminant sets. Obstructions to the integrability of admissible weight systems to…

Mean curvature flow evolves isometrically immersed base manifolds $M$ in the direction of their mean curvatures in an ambient manifold $\bar{M}$. If the base manifold $M$ is compact, the short time existence and uniqueness of the mean…

Let $X_1^t$ and $X_2^t$ be volume preserving Anosov flows on a 3-dimensional manifold $M$. We prove that if $X_1^t$ and $X_2^t$ are $C^0$ conjugate then the conjugacy is, in fact, smooth, unless $M$ is a mapping torus of an Anosov…

We study uniformization problems for compact manifolds that arise as quotients of domains in complex flag varieties by images of Anosov homomorphisms. We focus on Anosov homomorphisms with "small" limit sets, as measured by the Riemannian…

A pair of transverse contact distributions on a 3-manifold will in general admit no 1-parameter families of symmetries: a flow preserving both contact distributions. Here, we will determine local normal forms for such pairs admitting…