Search results for "Extremal length"

Analytic Properties of Quasiconformal Mappings Between Metric Spaces

2012

We survey recent developments in the theory of quasiconformal mappings between metric spaces. We examine the various weak definitions of quasiconformality, and give conditions under which they are all equal and imply the strong classical properties of quasiconformal mappings in Euclidean spaces. We also discuss function spaces preserved by quasiconformal mappings.

Quasiconformal distortion on arcs

1994

On a fundamental variational lemma for extremal quasiconformal mappings

1986

Extremal length and Hölder continuity of conformal mappings

1986

Uniform continuity of quasiconformal mappings and conformal deformations

2008

We prove that quasiconformal maps onto domains satisfying a suitable growth condition on the quasihyperbolic metric are uniformly continuous even when both domains are equipped with internal metric. The improvement over previous results is that the internal metric can be used also in the image domain. We also extend this result for conformal deformations of the euclidean metric on the unit ball of R n \mathbb {R}^n .

Application of spaces of subspheres to conformal invariants of curves and canal surfaces

2013

Quasilines and conformal mappings

1981

Conformal curvatures of curves in

2001

Abstract We define a complete set of conformal invariants for pairs of spheres in and obtain from these the expressions of the conformal curvatures of curves in (n + 1)-space in terms of the Euclidean invariants.

Lipschitz conditions,b-arcwise connectedness and conformal mappings

1982

Generalized evolutes, vertices and conformal invariants of curves in Rn + 1

1999

Abstract We define the generalized evolute of a curve in ( n + 1)-space and find a duality relation between them. We also prove that the conformal torsion is a function of the speed of the generalized evolute and that the singular points of the generalized evolute (vertices) are conformal invariants.