Spaces with Conformal Dimension Greater than One

Spaces and Groups with Conformal Dimension Greater than One

We show that if a complete, doubling metric space is annularly linearly connected then its conformal dimension is greater than one, quantitatively. As a consequence, we answer a question of Bonk and Kleiner: if the boundary of a one-ended hyperbolic group has no local cut points, then its conformal dimension is greater than one.

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...

Conformal Dimension and the Quasisymmetric Geometry of Metric Spaces

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...

Homotopes and Conformal Deformations of Symmetric spaces

Homotopy is an important feature of associative and Jordan algebraic structures: such structures always come in families whose members need not be isomorphic among other, but still share many important properties. One may regard homotopy as a special kind of deformation of a given algebraic structure. In this work, we investigate the global counterpart of this phenomenon on the geometric level ...