Related papers: Perturbed cone theorems for proper harmonic maps

We show that the image of a nonconstant conformal harmonic map $\mathbb C\to \mathbb R^3$, not necessarily proper and possibly with branch points, intersects every properly embedded nonflat minimal surface of bounded curvature in $\mathbb…

We give a proof, using harmonic maps from disks to real trees, of Skora's theorem (Morgan-Otal (1993), Skora (1990), originally conjectured by Shalen): if G is the fundamental group of a surface of genus at least 2, then any small minimal…

A new general approach is introduced for definining an optimum zero-order Hamiltonian for Rayleigh-Schr\"odinger perturbation theory. Instead of taking the operator directly from a model problem, it is constructed to be a best fit to the…

In this paper we investigate the space of harmonic maps from a 2-torus to $\mathbb{S}^3$ using the spectral curve correspondence and Whitham deformations. In an open and dense subset of a parameter space we find that the space of harmonic…

This paper is a study of harmonic maps from Riemannian polyhedra to (locally) non-positively curved geodesic spaces in the sense of Alexandrov. We prove Liouville-type theorems for subharmonic functions and harmonic maps under two different…

In this paper we are concerned with the space of tempered ultrahyperfunctions corresponding to a proper open convex cone. A holomorphic extension theorem (the version of the celebrated edge of the wedge theorem) will be given for this…

We show the regularity of, and derive a-priori estimates for (weakly) harmonic maps from a Riemannian manifold into a Euclidean sphere under the assumption that the image avoids some neighborhood of a half-equator. The proofs combine…

In a previous work arXiv:physics/0611108v2, it was shown that the volume spanned by a molecular system in its conformational space can be effectively bounded by a polyhedral cone, this cone is described by means of a simple combinatorial…

Pseudo-Hermitian (including $\mathcal{PT}$-symmetric) field theories support phenomenology that cannot be replicated in standard Hermitian theories. We describe a concrete example in which the vortex solutions that are realised in a…

$\alpha$-Dirac-harmonic maps are variations of Dirac-harmonic maps, analogous to $\alpha$-harmonic maps that were introduced by Sacks-Uhlenbeck to attack the existence problem for harmonic maps from surfaces. For $\alpha >1$, the latter are…

We investigate the properties of a class of piecewise-fractional maps arising from the introduction of an invariance under rescaling into convex quadratic maps. The subsequent maps are quasiconvex, and pseudoconvex on specific convex cones;…

Harmonic morphisms, maps which preserve Laplace's equation, are intimately connected to the topic of minimal submanifolds. In this article we first characterise harmonic morphisms between Riemannian manifolds as the weakly horizontally…

This paper focuses on distinguishing classes of dynamical behavior for one- and two-dimensional torus maps, in particular between orbits that are incommensurate, resonant, periodic, or chaotic. We first consider Arnold's circle map, for…

A new so-called `gravitational loss-cone instability' in stellar systems has recently been investigated theoretically in the framework of linear perturbation theory and proved to be potentially important in understanding the physical…

We establish a coarse version of the Cartan-Hadamard theorem, which states that proper coarsely convex spaces are coarsely homotopy equivalent to the open cones of their ideal boundaries. As an application, we show that such spaces satisfy…

A recent result of Condon, Kim, K\"{u}hn and Osthus implies that for any $r\geq (\frac{1}{2}+o(1))n$, an $n$-vertex almost $r$-regular graph $G$ has an approximate decomposition into any collections of $n$-vertex bounded degree trees. In…

We prove the existence and uniqueness of harmonic maps in degree one homotopy classes of closed, orientable surfaces of positive genus, when the target has conic points with cone angles less than $2\pi$. For a cone point $p$ of cone angle…

Let ${\mathcal A}$ be a nonempty real central arrangement of hyperplanes and ${\rm \bf Ch}$ be the set of chambers of ${\mathcal A}$. Each hyperplane $H$ defines a half-space $H^{+} $ and the other half-space $H^{-}$. Let $B = \{+, -\}$.…

In this paper, we generalize the existence result in [14] and prove convergence theorems of the iterative scheme in [12, 16] for monotone generalized alpa-nonexpansive mappings in uniformly convex partially ordered hyperbolic metric spaces.…

Three types of orbits are theoretically possible in autonomous Hamiltonian systems with three degrees of freedom: fully chaotic (they only obey the energy integral), partially chaotic (they obey an additional isolating integral besides…