Extremal Discs and the Regularity of CR Mappings in Higher Codimension

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...

Extremal Discs and the Regularity of Cr Mappingsin Higher Codimensiona

Extremal Discs and the Regularity of Cr Mappingsin Higher

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...

Vector Field Construction of Segre Sets

§1. Geometry of finite type and review of CR-extension theory . . . . .2. §2. Identification of CR vector fields and of Segre varieties . . . . . . . . . .4. §3. Segre varieties and extrinsic complexification . . . . . . . . . . . . . . . . . . . .10. §4. Segre sets and iterated complexifications . . . . . . . . . . . . . . . . . . . . . . . . .12. §5. Segre varieties and conjugate Segre variet...