Related papers: Snowballs are Quasiballs
In the Euclidean unit three-ball, we construct compact, embedded, two-sided free boundary minimal surfaces with connected boundary and prescribed high genus, by a gluing construction tripling the equatorial disc. Aside from the equatorial…
We discuss various scattering properties of non-topological solitons, Q-balls, on potential obstructions in (1+1) and (2+1) dimensions. These obstructions, barriers and holes, are inserted into the potential of the theory via the coupling…
We introduce the quasi-hyperbolicity constant of a metric space, a rough isometry invariant that measures how a metric space deviates from being Gromov hyperbolic. This number, for unbounded spaces, lies in the closed interval $[1,2]$. The…
We define two transforms between non-conformal harmonic maps from a surface into the 3-sphere. With these transforms one can construct, from one such harmonic map, a sequence of harmonic maps. We show that there is a correspondence between…
Let $S$ be a complete flat surface, such as the Euclidean plane. We determine the homeomorphism class of the space of all curves on $S$ which start and end at given points in given directions and whose curvatures are constrained to lie in a…
We study the local regularity of sliding almost minimal sets of dimension 2 in $R^n$ , bounded by a smooth curve $L$. These are a good way to model soap films bounded by a curve, and their definition is similar to Almgren's. We aim for a…
The object under study is a particular closed curve on the square lattice $\Z^2$ related with the Fibonacci sequence $F_n$. It belongs to a class of curves whose length is $4F_{3n+1}$, and whose interiors by translation tile the plane. The…
We characterize conformally removable sets in the plane with the aid of the recent developments in the theory of metric surfaces. We prove that a compact set in the plane is $S$-removable if and only if there exists a quasiconformal map…
Roughly speaking, let us say that a map between metric spaces is large scale conformal if it maps packings by large balls to large quasi-balls with limited overlaps. This quasi-isometry invariant notion makes sense for finitely generated…
Suppose that $X$ and $Y$ are quasiconvex and complete metric spaces, that $G\subset X$ and $G'\subset Y$ are domains, and that $f: G\to G'$ is a homeomorphism. In this paper, we first give some basic properties of short arcs, and then we…
We show that $\mathbb{C}^2$ contains pairs of properly embedded, smooth complex curves that are isotopic through homeomorphisms but not diffeomorphisms of $\mathbb{C}^2$. The construction is based on realizing corks as branched covers of…
For some class of mappings, which are generalization of space quasiisometries, an upper estimate for a measure of image of a ball is obtained. As consequence, it is obtained one analog of Schwartz lemma for mappings mentioned above. Results…
We perform a general analysis of thin-wall Q-balls in AdS space. We provide numeric solutions and highly accurate analytic approximations over much of the parameter space. These analytic solutions show that AdS Q-balls exhibit significant…
The last half century of research into the structure, dynamics, and thermodynamics of simple liquids has revealed a number of approximate universalities. This paper argues that simple liquids' reduced-coordinate constant-potential-energy…
We present numerical evidence for the existence of spinning generalizations for non-topological Q-ball solitons in the theory of a complex scalar field with a non-renormalizable self-interaction. To the best of our knowledge, this provides…
The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
Although the hyperbolic metric possesses many remarkable properties, it is not defined on arbitrary subdomains of $\mathbb{R}^n$ with $n \geq 2$. This article introduces a new hyperbolic-type metric that provides an alternative approach to…
Several natural complex configuration spaces admit surprising uniformizations as arithmetic ball quotients, by identifying each parametrized object with the periods of some auxiliary object. In each case, the theory of canonical models of…
It is well known that a three dimensional (closed, connected and compact) manifold is obtained by identifying boundary faces from a polyhedron P. The study of (\partial P)/~, the boundary \partial P with the polygonal faces identified in…
We consider the triangular ratio metric and estimate the radius of convexity for balls in some special domains and prove the inclusion relations of metric balls defined by the triangular ratio metric, the quasihyperbolic metric and the…