5 Extremal Discs and Analytic Continuation of Product Cr Maps

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...

Analytic Discs, Global Extremal Functions and Projective Hulls in Projective Space

Using a recent result of Lárusson and Poletsky regarding plurisubharmonic subextensions we prove a disc formula for the quasiplurisubharmonic global extremal function for domains in P. As a corollary we get a characterization of the projective hull for connected compact sets in P by the existence of analytic discs.

Extremal Discs and the Regularity of Cr Mappingsin Higher Codimensiona

Extremal Discs and the Regularity of Cr Mappingsin Higher