Related papers: Bi-Lipschitz quasiconformal extensions

We introduce curvature-adapted foliations of complex hyperbolic space and study some of their properties. Generalized pseudo-Einstein hypersurfaces of complex hyperbolic space are classified. Analogous results for curvature-adapted…

We investigate the Bilinear Hilbert Transform in the plane and the pointwise convergence of bilinear averages in Ergodic theory, arising from $\Z^2$ actions. Our techniques combine novel one and a half dimensional phase-space analysis with…

Here we give an alternate proof of a sufficient condition due to J. Mateu, J. Orobitg, and J. Verdera for a quasiconformal map of the plane with dilatation supported in a smooth domain to be bi-Lipschitz. We also extend this theorem to…

We prove that, given a planar bi-Lipschitz homeomorphism $u$ defined on the boundary of the unit square, it is possible to extend it to a function $v$ of the whole square, in such a way that $v$ is still bi-Lipschitz. In particular,…

We extend Donaldson's asymptotically holomorphic techniques to symplectic orbifolds. More precisely, given a symplectic orbifold such that the symplectic form defines an integer cohomology class, we prove that there exist sections of large…

We present a complete classification of complex plane algebraic curves, equipped with the induced Euclidean, up to global bilipschitz homeomorphism.

We construct self-adjoint Laplacians and symmetric Markov semigroups on partially hyperbolic attractors and on hyperbolic attractors with singularities, endowed with Gibbs u-measures. If the measure has full support, we can also guarantee…

This is a tale describing the large scale geometry of Euclidean plane domains with their hyperbolic or quasihyperbolic distances. We prove that in any hyperbolic plane domain, hyperbolic and quasihyperbolic quasi-geodesics are the same…

We devise variants of classical nonconforming methods for symmetric elliptic problems. These variants differ from the original ones only by transforming discrete test functions into conforming functions before applying the load functional.…

This paper begins by introducing the concept of a quasi-hom-Lie algebra which is a natural generalization of hom-Lie algebras introduced in a previous paper by the authors. Quasi-hom-Lie algebras include also as special cases (color) Lie…

We study quasisymmetric maps, which act on the boundary of the hyperbolic plane, by looking at their action on the Farey triangulation. Our main results identify exactly which quasisymmetric maps correspond to pinched lambda lengths in…

We provide a complete characterization of those self-homeomorphisms of the unit circle that admit homeomorphic extensions to the unit disk belonging to bi--Orlicz--Sobolev spaces. Our results generalize classical criteria from the Sobolev…

We construct self-adjoint Laplacians and symmetric Markov semigroups on hyperbolic attractors, endowed with Gibbs $u$-measures. If the measure has full support, we can also conclude the existence of an associated symmetric diffusion…

Convexity properties of Weil-Petersson geodesics on the Teichm\"{u}ller space of punctured Riemann surfaces are investigated. A normal form is presented for the Weil-Petersson Levi-Civita connection for pinched hyperbolic metrics. The…

We study the boundary correspondence under $\mu$-homeomorphisms $f$ of the open upper half-plane onto itself. Sufficient conditions are given for $f$ to admit a homeomorphic extension to the closed half-plane with prescribed boundary…

We present different constructions of abstract boundaries for bounded complete (Kobayashi) hyperbolic domains in ${\mathbb C}^d$, $d \geq 1$. These constructions essentially come from the geometric theory of metric spaces. We also present,…

An Hermitian bounded symmetric domain in a complex vector space, given in its circled realization, is endowed with two natural symplectic forms: the flat form and the hyperbolic form. In a similar way, the ambient vector space is also…

We first identify (up to linear isomorphism) the Lipschitz free spaces of quasiarcs. By decomposing quasiconformal trees into quasiarcs as done in an article of David, Eriksson-Bique, and Vellis, we then identify the Lipschitz free spaces…

This is a survey about certain "almost homomorphisms" and "almost linear" functionals (called quasi-morphisms and quasi-states) in symplectic topology and their applications to Hamiltonian dynamics, functional-theoretic properties of…

In this article, we examine stretching and rotation of planar quasiconformal mappings on a line. We show that for almost every point on the line, the set of complex stretching exponents (describing stretching and rotation jointly) is…