Related papers: Reshetnyak-class mappings and composition operator…

We investigate the mapping class group of an orientable $\omega$-bounded surface. Such a surface splits, by Nyikos's Bagpipe Theorem, into a union of a bag (a compact surface with boundary) and finitely many long pipes. The subgroup…

The classical theorems of Banach and Stone, Gelfand and Kolmogorov, and Kaplansky show that a compact Hausdorff space $X$ is uniquely determined by the linear isometric structure, the algebraic structure, and the lattice structure,…

Let $G$ and $\Omega$ be two planar domains. We give necessary and sufficient conditions on a sequence $(\phi_n)$ of eventually injective holomorphic mappings from $G$ to $\Omega$ for the existence of a function $f\in H(\Omega)$ whose orbit…

In this work we investigate the Sobolev space $\mathrm{H}^{1}(\partial\Omega)$ on a strong Lipschitz boundary $\partial\Omega$, i.e., $\Omega$ is a strong Lipschitz domain. In most of the literature this space is defined via charts and…

We study the approximation of functions that map a Euclidean domain $\Omega\subset \mathbb{R}^{d}$ into an $n$-dimensional Riemannian manifold $(M,g)$ minimizing an elliptic, semilinear energy in a function set $H\subset W^{1,2}(\Omega,M)$.…

From the `cofree' cooperad $T'(A[-1])$ on a collection $A$ together with a differential, we construct an $L_\infty$-algebra structure on the total space $\bigoplus_nA(n)$ that descends to coinvariants. We use this construction to define an…

Given a smooth complete Riemannian manifold with bounded geometry $(M,g)$ and a linear connection $\nabla$ on it (not necessarily a metric one), we prove the $L^p$-boundedness of operators belonging to the global pseudo-differential classes…

This article tackles the problem of the classification of expansive homeomorphisms of the plane. Necessary and sufficient conditions for a homeomorphism to be conjugate to a linear hyperbolic automorphism will be presented. The techniques…

Let $N=(\Omega,\sigma)$ and $M=(\Omega^*,\rho)$ be doubly connected Riemann surfaces and assume that $\rho$ is a smooth metric with bounded Gauss curvature $\mathcal{K}$ and finite area. The paper establishes the existence of homeomorphisms…

We present an analogue to the Majorisation Theorem of Reshetnyak in the setting of Lorentzian length spaces with upper curvature bounds: given two future-directed timelike rectifiable curves $\alpha$ and $\beta$ with the same endpoints in a…

Let $(X, \omega)$ be a compact symplectic manifold and $L$ be a Lagrangian submanifold. Suppose $(X, L)$ has a Hamiltonian $S^1$ action with moment map $\mu$. Take an invariant $\omega$-compatible almost complex structure, we consider…

Let $\mathcal{X}$ be a metric space with doubling measure and $L$ a one-to-one operator of type $\omega$ having a bounded $H_\infty$-functional calculus in $L^2(\mathcal{X})$ satisfying the reinforced $(p_L, q_L)$ off-diagonal estimates on…

We provide a condition on a set of directions $\Omega \subset \mathbb{S}^1$ ensuring that the associated directional maximal operator $M_\Omega$ is unbounded on $L^p(\mathbb{R}^2)$ for every $1 \leq p < \infty$. The techniques of proof…

We investigate the compactness of composition operators on the Hardy space of Dirichlet series induced by a map $\varphi(s)=c_0s+\varphi_0(s)$, where $\varphi_0$ is a Dirichlet polynomial. Our results depend heavily on the characteristic…

Let $\Omega$ be an open subset of $\Ri^d$ with $0\in \Omega$. Further let $H_\Omega=-\sum^d_{i,j=1}\partial_i\,c_{ij}\,\partial_j$ be a second-order partial differential operator with domain $C_c^\infty(\Omega)$ where the coefficients…

Let $G$ be a simply connected nilpotent Lie group with Lie algebra $\frak g$; let $\frak g^*$ be the dual of $\frak g$. Let $\Omega$ be a locally compact second countable Hausdorff space with a continuous $G$ action, and let $C^*(G,\Omega)$…

We work in a class of Sobolev $W^{1,p}$ maps, with $p > d-1$, from a bounded open set $\Omega \subset \mathbb{R}^{d}$ to $\mathbb{R}^{d}$ that do not exhibit cavitation and whose trace on $\partial \Omega$ is also $W^{1,p}$. Under the…

Let $\Omega\subset\mathbb{R}^{n+1}$, $n\ge 2$, be a 1-sided chord-arc domain, that is, a domain which satisfies interior Corkscrew and Harnack Chain conditions (these are respectively scale-invariant/quantitative versions of the openness…

We define abstract Sobolev type spaces on $\mathsf{L}^p$-scales, $p\in [1,\infty)$, on Hermitian vector bundles over possibly noncompact manifolds, which are induced by smooth measures and families $\mathfrak{P}$ of linear partial…

We study power boundedness and related properties such as mean ergodicity for (weighted) composition operators on function spaces defined by local properties. As a main application of our general approach we characterize when (weighted)…