相关论文: Construction of nearly hyperbolic distance on punc…

The length of the shortest closed geodesic in a hyperbolic surface $X$ is called the systole of $X.$ When $X$ is an $n$-times punctured sphere $\hat{ \mathbb{C}} \setminus A$ where $A \subset \hat{\mathbb{C}}$ is a finite set of cardinality…

The goal of this paper is to prove the conjecture of Krzyz posed in 1968 that for nonvanishing holomorphic functions $f(z) = c_0 + c_1 z + ...$ in the unit disk with $|f(z)| \le 1$, we have the sharp bound $|c_n| \le 2/e$ for all $n \ge 1$,…

We give a distance estimate for the metric on the disk complex and show that it is Gromov hyperbolic. As another application of our techniques, we find an algorithm which computes the Hempel distance of a Heegaard splitting, up to an error…

We prove that, among the polygons in a punctured disc with fixed angles, the perimeter is minimized by the polygon with an inscribed horocycle centered at the puncture. We generalize this to a disc with a cone point and to an annulus with a…

We establish a correspondence on a Riemann surface between hyperbolic metrics with isolated singularities and bounded projective functions whose Schwarzian derivatives have at most double poles and whose monodromies lie in ${\rm…

We find bounds for the length of the systole -- the shortest essential, non-peripheral closed curve -- for arithmetic punctured spheres with $n$ cusps, for $n=4$ through $n=12$, some of which were previously known due to Schmutz. This is…

Complete hyperbolicity of small Euclidean balls with respect to a C^1-smooth almost complex structure standard at origin is improved to give a complete hyperbolicity of strictly pseudoconvex domains. More precise (and lower) regularity…

In practical purposes for some geometrical problems in computer science we have as information the coordinates of some finite points in surface instead of the whole body of a surface. The problem arised here is: "How to define a distance…

We prove an inequality which quantifies the idea that a holomorphic self-map of the disc that perturbs two points is close to the identity function.

For a hyperbolic fibered 3-manifold M, we prove results that uniformly relate the structure of surface projections as one varies the fibrations of M. This extends our previous work from the fully-punctured to the general case.

We give an alternative definition of relative hyperbolicity based on properties of closest-point projections on peripheral subgroups. We also derive a distance formula for relatively hyperbolic groups, similar to the one for mapping class…

For the moduli space of the punctured spheres, we find a new equality between two symplectic forms defined on it. Namely, by treating the elements of this moduli space as the singular Euclidean metrics on a sphere, we give an interpretation…

We study the growth of hyperbolic type distances in starlike domains. We derive estimates for various hyperbolic type distances and consider the asymptotic sharpness of the estimates.

We study the Riemannian distance function from a fixed point (a point-wise target) of Euclidean space in the presence of a compact obstacle bounded by a smooth hypersurface. First, we show that such a function is locally semiconcave with a…

Consider a set P of N random points on the unit sphere of dimension $d-1$, and the symmetrized set S = P union (-P). The halving polyhedron of S is defined as the convex hull of the set of centroids of N distinct points in S. We prove that…

In 1968, Krzyz conjectured that for non-vanishing holomorphic functions $f(z) = c_0 + c_1 z + \dots$ in the unit disk with $|f(z)| \leq 1$, we have the sharp bound $|c_n| \leq 2/e$ for all $n \geq 1$, with equality only for the function…

The scheme for construction of distances, presented in the previous paper quant-ph/0005087, v.1 (Ref. 1) is amended. The formulation of Proposition 1 of Ref. 1 does not ensure the triangle inequality, therefore some of the functionals…

In this paper we present a method for constructing the continuous best fractal approximation in the space of bounded functions. We construct the finite-dimensional subspace of the space of bounded functions whose base consists of the…

In this paper, we prove a geometrical inequality which states that for any four points on a hemisphere with the unit radius, the largest sum of distances between the points is 4+4*sqrt(2). In our method, we have constructed a rectangular…

Based on a well known Sh.-T. Yau theorem we obtain that the real part of a holomorphic function on a K\"{a}hler manifold with the Ricci curvature bounded from below by $-1$ is contractive with respect to the distance on the manifold and the…