Related papers: Asymptotic values of hyperbolic monopoles

We show that a partially hyperbolic system can have at most a finite number of compact center-stable submanifolds. We also give sufficient conditions for these submanifolds to exist and consider the question of whether they can intersect…

We establish isosystolic inequalities for a class of manifolds which includes the aspherical manifolds. In particular, we relate the systolic volume of aspherical manifolds first to their minimal entropy, then to the algebraic entropy of…

We analyze the resolvent and define the scattering matrix for asymptotically hyperbolic manifolds with metrics which have a polyhomogeneous expansion near the boundary, and also prove that there is always an essential singularity of the…

We establish sharp bounds on the mixing rates of a class of two dimensional non-uniformly hyperbolic symplectic maps. This provides a primer on how to investigate such questions in a concrete example and, at the same time, it solves a…

We study the moduli space for an arbitrary number of BPS monopoles in a gauge theory with an arbitrary gauge group that is maximally broken to $U(1)^k$. From the low energy dynamics of well-separated dyons we infer the asymptotic form of…

We prove that for certain partially hyperbolic skew-products, non-uniform hyperbolicity along the leaves implies existence of a finite number of ergodic absolutely continuous invariant probability measures which describe the asymptotics of…

Some results are proved concerning asymptotic and deficient values in connection with the second order linear differential equation $y'' + Ay = 0$, in which the coefficient $A$ is entire.

In this paper we present an overview of results for discrete trigonometric and hyperbolic systems. These systems are discrete analogues of trigonometric and hyperbolic linear Hamiltonian systems. We show results which can be viewed as…

We provide an elementary proof of the asymptotic behavior of solutions of second order differential equations.

We compute the asymptotics of the determinants of certain $n\times n$ Toeplitz + Hankel matrices $T_n(a)+H_n(b)$ as $n\to\infty$ with symbols of Fisher-Hartwig type. More specifically we consider the case where $a$ has zeros and poles and…

We prove that, among weighted isotropic perimeters, only constant multiples of the Euclidean perimeter satisfy the monotonicity property on nested convex bodies. Although the analogous result fails for general weighted anisotropic…

We give necessary and sufficient conditions for a hyperbolic set to be non-chaotic (or, conversely, chaotic) in a certain sense.

Asymptotic results for weighted floating bodies are established and used to obtain new proofs for the existence of floating areas on the sphere and in hyperbolic space and to establish the existence of floating areas in Hilbert geometries.…

The hyperbolic structure on a 3-dimensional cone-manifold with a knot as singularity can often be deformed into a limiting Euclidean structure. In the present paper we show that the respective normalised Euclidean volume is always an…

For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…

We prove that every finite group is the orientation-preserving isometry group of the complement of a hyperbolic link in the 3-sphere.

We prove logarithm laws for unipotent flows on non-compact finite-volume hyperbolic manifolds. Our method depends on the estimate of norms of certain incomplete Eisenstein series.

Label inventories for fine-grained entity typing have grown in size and complexity. Nonetheless, they exhibit a hierarchical structure. Hyperbolic spaces offer a mathematically appealing approach for learning hierarchical representations of…

Solitons in one-dimensional parity-time (PT)-symmetric periodic potentials are studied using exponential asymptotics. The new feature of this exponential asymptotics is that, unlike conservative periodic potentials, the inner and outer…

We calculate the asymptotic value of the choice number of complete multi-partite graphs.