Search results for "Conformal map"
showing 5 items of 125 documents
Geodesic flow of the averaged controlled Kepler equation
2008
A normal form of the Riemannian metric arising when averaging the coplanar controlled Kepler equation is given. This metric is parameterized by two scalar invariants which encode its main properties. The restriction of the metric to $\SS^2$ is shown to be conformal to the flat metric on an oblate ellipsoid of revolution, and the associated conjugate locus is observed to be a deformation of the standard astroid. Though not complete because of a singularity in the space of ellipses, the metric has convexity properties that are expressed in terms of the aforementioned invariants, and related to surjectivity of the exponential mapping. Optimality properties of geodesics of the averaged controll…
Canal foliations of S 3
2012
The goal of the article is to classify foliations of S3 by regular canal surfaces, that is envelopes of one-parameter families of spheres which are immersed surfaces. We will add some extra information when the leaves are “surfaces of revolution” in a conformal sense.
Lectures on quasiconformal and quasisymmetric mappings
2009
Weighted Hardy Spaces of Quasiconformal Mappings
2019
We establish a weighted version of the $H^p$-theory of quasiconformal mappings.
Openness and Discreteness
2013
The aim of this chapter is to study conditions under which a mapping of finite distortion is open (maps open sets to open sets) and discrete (preimage of each point is a discrete set).