Search results for "hyperbolic"

Boundary Behavior of Harmonic Functions on Gromov Hyperbolic Manifolds

2013

Total curvatures of convex hypersurfaces in hyperbolic space

1999

We give sharp upper estimates for the difference circumradius minus inradius and for the angle between the radial vector (respect to the center of an inball) and the normal to the boundary of a compact $h$-convex domain in the hyperpolic space. We apply these estimates to get the limit at the infinity for the quotients Volume/Area and (Total $k$-mean curvature)/Area of a family of $h$-convex domains which expand over the whole space. The theorem for the first quotient gives an extension to arbitrary dimension of a result of Santalo and Yanez for the hyperbolic plane.

THE HOROSPHERICAL GEOMETRY OF SUBMANIFOLDS IN HYPERBOLIC SPACE

2005

Some geometrical properties associated to the contact of submanifolds with hyperhorospheres in hyperbolic -space are studied as an application of the theory of Legendrian singularities.

Sobolev homeomorphic extensions

2021

Let $\mathbb X$ and $\mathbb Y$ be $\ell$-connected Jordan domains, $\ell \in \mathbb N$, with rectifiable boundaries in the complex plane. We prove that any boundary homeomorphism $\varphi \colon \partial \mathbb X \to \partial \mathbb Y$ admits a Sobolev homeomorphic extension $h \colon \overline{\mathbb X} \to \overline{\mathbb Y}$ in $W^{1,1} (\mathbb X, \mathbb C)$. If instead $\mathbb X$ has $s$-hyperbolic growth with $s>p-1$, we show the existence of such an extension lies in the Sobolev class $W^{1,p} (\mathbb X, \mathbb C)$ for $p\in (1,2)$. Our examples show that the assumptions of rectifiable boundary and hyperbolic growth cannot be relaxed. We also consider the existence of $W^{…

Non-equivalent hyperbolic knots

2002

We construct, for each integer n 3, pairs of non-equivalent hyperbolic knots with the same 2fold and n-fold cyclic branched covers. We also discuss necessary conditions for such pairs of knots to exist.  2001 Elsevier Science B.V. All rights reserved. MSC: primary 57M25; secondary 57M12, 57M50

Eckhaus instability of stationary patterns in hyperbolic reaction–diffusion models on large finite domains

2022

AbstractWe have theoretically investigated the phenomenon of Eckhaus instability of stationary patterns arising in hyperbolic reaction–diffusion models on large finite domains, in both supercritical and subcritical regime. Adopting multiple-scale weakly-nonlinear analysis, we have deduced the cubic and cubic–quintic real Ginzburg–Landau equations ruling the evolution of pattern amplitude close to criticality. Starting from these envelope equations, we have provided the explicit expressions of the most relevant dynamical features characterizing primary and secondary quantized branches of any order: stationary amplitude, existence and stability thresholds and linear growth rate. Particular em…

On some inequalities for the identric, logarithmic and related means

2015

We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.

Substitution–dilution method to correct the matrix effect in multi-element quantitative analysis by X-ray fluorescence

2001

Abstract A mathematical model based on the dilution–addition method (DAM) for multi-elemental analysis using an X-ray fluorescence technique is proposed. The conditions for sample preparation do not require both the unknown and standard samples to be similar in composition and mineralogy, and the unknown sample is replaced quantitatively by the standard sample, hence the denomination substitution–dilution method (SDM). This method makes it possible to correct the matrix effect in multi-elemental quantitative analysis by X-ray fluorescence for each analyte. The proposed model presents hyperbolic behaviour of the experimental data when the X-ray fluorescence intensities are represented versus…

Description of the retention behaviour of solutes in micellar liquid chromatography with organic modifiers: Comparison of two methods

1995

Two methods for the description of the retention behaviour of solutes in micellar liquid chromatography are compared. One of them divides the parameter space into triangular subspaces, fitting a different equation in each subspace. The second method makes use of a unique equation, valid in the whole parameter space. In both cases, equations of the type log k=f (μ, ϕ), and 1/k=f (μ, ϕ), (μ and ϕ are the concentration of surfactant and alcohol, respectively), were used to describe the retention. The use of the hyperbolic function, 1/k=c0+c1μ+c3μϕ, to describe the whole parameter space yielded the best prediction. When a small portion of the parameter space was modelled, a simpler hyperbolic f…

Integral binary Hamiltonian forms and their waterworlds

2018

We give a graphical theory of integral indefinite binary Hamiltonian forms $f$ analogous to the one by Conway for binary quadratic forms and the one of Bestvina-Savin for binary Hermitian forms. Given a maximal order $\mathcal O$ in a definite quaternion algebra over $\mathbb Q$, we define the waterworld of $f$, analogous to Conway's river and Bestvina-Savin's ocean, and use it to give a combinatorial description of the values of $f$ on $\mathcal O\times\mathcal O$. We use an appropriate normalisation of Busemann distances to the cusps (with an algebraic description given in an independent appendix), and the $\operatorname{SL}_2(\mathcal O)$-equivariant Ford-Voronoi cellulation of the real …