Spaces and Groups with Conformal Dimension Greater than One

Spaces with Conformal Dimension Greater than One

We show that if a complete, doubling metric space is annulus linearly connected then its conformal dimension is greater than one, quantitatively. As a consequence, hyperbolic groups whose boundaries have no local cut points have conformal dimension greater than one; this answers a question of Bonk and Kleiner.

ar X iv : m at h - ph / 0 50 90 42 v 1 1 9 Se p 20 05 1 GENERALIZATION OF CONFORMAL TRANSFORMATIONS

Conformal transformations of a Euclidean (complex) plane have some kind of completeness (sufficiency) for the solution of many mathematical and physical-mathematical problems formulated on this plane. There is no such completeness in the case of Euclidean, pseudo-Euclidean and polynumber spaces of dimension greater than two. In the present paper we show that using the concepts of analogical geo...

3D-Conformal Radiation Therapy and Intensity-Modulated Radiation Therapy Techniques for Laryngeal Cancer Taking Parotid Glands as Organ at Risk

Background: Three-dimensional conformal radiotherapy (3D-CRT) and intensity-modulated radiotherapy (IMRT) techniques are used for the treatment of patients with laryngeal cancer. Objective: This study aimed to investigate the effects of these 2 treatment techniques on the planning target volume (PTV) (laryngeal cancer), dose homogeneity, dose of organs at...

Conformal dimension and canonical splittings of hyperbolic groups

We prove a general criterion for a metric space to have conformal dimension one. The conditions are stated in terms of the existence of enough local cut points in the space. We then apply this criterion to the boundaries of hyperbolic groups and show an interesting relationship between conformal dimension and some canonical splittings of the group.

Conformal Dimension and the Quasisymmetric Geometry of Metric Spaces