Related papers: On the harmonic M\"obius transformations

In the paper we discuss conformable derivative behavior in arbitrary Banach spaces and clear the connection between two conformable derivatives of different order. As a consequence we obtain the important result that an abstract function…

The theory of symmetry of quantum mechanical systems is applied to study the structure and properties of several classes of relevant maps in quantum information theory: CPTP, PPT and Schwarz maps. First, we develop the general structure…

Transports preserving the angle between two contravariant vector fields but changing their lengths proportional to their own lengths are introduced as ''conformal'' transports and investigated over spaces with contravariant and covariant…

We consider a non-negative self-adjoint operator L satisfying generalized Gaussian estimates on a doubling metric measure space, and show that if L has a spectral gap then the local and global Hardy spaces defined by means of appropriate…

A harmonic mapping $f=h+\overline{g}$ in $\mathbb{D}$ is $\varphi$-normal if $f^{\#}(z)=\mathcal{O}(|\varphi(z)|), \text{ as } |z|\to 1^-,$ where $f^{\#}(z)={(|h'(z)|+|g'(z)|)}/{(1+|f(z)|^2)}.$ In this paper, we establish several sufficient…

We use the density function of a harmonic space to obtain estimates for the eigenvalues of the Jacobi operator; when these estimates are sharp, then the harmonic space is a symmetric Osserman space.

For the Hamiltonian operator H = -{\Delta}+V(x) of the Schr\"odinger Equation with a repulsive potential, the problem of local decay is considered. It is analyzed by a direct method, based on a new, L^2 bounded, propagation observable. The…

In this paper, the boundedness and compactness of the difference of composition-differentiation operators $D_\varphi-D_\psi$ acting from Hardy spaces $H^p$ to weighted Bergman spaces $A^q_\alpha$ are completely characterize for all…

A many particle Hamiltonian, where the interaction term conserves the number of particles, is considered. A master equation for the populations of the different levels is derived in an exact way. It results in a local equation with…

Let $\varphi$ be a univalent non-elliptic self-map of the unit disc $\mathbb D$ and let $(\psi_{t})$ be a continuous one-parameter semigroup of holomorphic functions in $\mathbb D$ such that $\psi_{1}\neq\mathrm{id}_{\mathbb D}$ commutes…

Let X be a set of analytic functions on the open unit disk D, and let phi be an analytic function on D such that phi(D) is contained in D and f |-> f o phi takes X into itself. We present conditions on X ensuring that if f |-> f o phi is…

We consider the initial-value problem for the equivariant Schr\"odinger maps near a family of harmonic maps. We provide some supplemental arguments for the proof of local well-posedness result by Gustafson, Kang and Tsai in [Duke Math. J.…

We consider the 1-harmonic flow of maps from a bounded domain into a submanifold of a Euclidean space, i.e. the gradient flow of the total variation functional restricted to maps taking values in the manifold. We restrict ourselves to…

Due to the invariance properties of cross-ratio, M\"obius transformations are often used to map a set of points or other geometric object into a symmetric position to simplify a problem studied. However, when the points are mapped under a…

We compare two relationships between quadratic differentials and measured geodesic laminations on hyperbolic Riemann surfaces (by foliations or complex projective structures). Each yields a homeomorphism $\ML(S) \to Q(X)$ for any conformal…

Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…

The primary aim of this paper is to characterize the uniformly locally univalent harmonic mappings in the unit disk. Then, we obtain sharp distortion, growth and covering theorems for one parameter family ${\mathcal B}_{H}(\lambda)$ of…

On a Riemannian surface, the energy of a map into a Riemannian manifold is a conformal invariant functional, and its critical points are the harmonic maps. Our main result is a generalization of this theorem when the starting manifold is…

Let p:N->M be a surjective map of smooth manifolds. We are concerned with singular perturbation problems associated to a pair of second order positive definite differential operators with no zero order terms, that are intertwined by p. We…

A salami is a connected, locally finite, weighted graph with non-negative Ollivier Ricci curvature and at least two ends of infinite volume. We show that every salami has exactly two ends and no vertices with positive curvature. We moreover…