Extremal Discs and the Regularity of Cr Mappingsin Higher

Extremal Discs and the Regularity of Cr Mappingsin Higher Codimensiona

Extremal Discs and the Regularity of CR Mappings in Higher Codimension

We develop a local theory of extremal analytic discs attached to a strictly pseudoconvex manifold of higher codimension in complex space. We then apply the results to prove the regularity of CR homeomorphisms of such manifolds.

On the Regularity of Cr Mappings in Higher Codimension

We give a proof of the regularity of Hölder CR homeomorphisms of strictly pseudo convex CR manifolds of higher codimension. The purpose of this paper is to complete and simplify the proof of one of the main results of [T] on the regularity of CR mappings of strictly pseudo convex CR manifolds of higher codimension. In [T] we introduce a local theory of extremal discs for such manifolds and appl...

Regularity and Extremality of Quasiconformal Homeomorphisms on Cr 3-manifolds

This paper first studies the regularity of conformal homeomorphisms on smooth locally embeddable strongly pseudoconvex CR manifolds. Then moduli of curve families are used to estimate the maximal dilatations of quasiconformal homeomorphisms. On certain CR 3-manifolds, namely, CR circle bundles over flat tori, extremal quasiconformal homeomorphisms in some homotopy classes are constructed. These...

5 Extremal Discs and Analytic Continuation of Product Cr Maps