Möbius invariant metrics bilipschitz equivalent to the hyperbolic metric

Möbius Invariant Metrics Bilipschitz Equivalent to the Hyperbolic Metric

We study three Möbius invariant metrics, and three affine invariant analogs, all of which are bilipschitz equivalent to the Poincaré hyperbolic metric. We exhibit numerous illustrative examples.

Möbius-invariant natural neighbor interpolation

The Apollonian Metric: Limits of the Comparison and Bilipschitz Properties

The Apollonian metric is a generalization of the hyperbolic metric introduced by Beardon [2]. It is defined in arbitrary domains in Rn and is Möbius invariant. Another advantage over the well-known quasihyperbolic metric [8] is that it is simpler to evaluate. On the downside, points cannot generally be connected by geodesics of the Apollonian metric. This paper is the last in a series of four p...

On a Metric on Translation Invariant Spaces

In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.

Length equivalent hyperbolic manifolds

In the case when M is an orientable Riemannian manifold of negative curvature L (M) and L(M) are related to the eigenvalue spectrum of M; that is, the set E (M) of all eigenvalues of the Laplace–Beltrami operator acting on L2(M) counted with multiplicities. For example, in this setting it is known that E (M) determines L(M) (see [3]). In the case of closed hyperbolic surfaces, the stronger stat...