Kaushal Verma

Boundary regularity of correspondences in ℂn

AbstractLetM, M′ be smooth, real analytic hypersurfaces of finite type in ℂn and

A note on uniform extendability of automorphisms

\hat f

Comments on the Green’s function of a planar domain

a holomorphic correspondence (not necessarily proper) that is defined on one side ofM, extends continuously up toM and mapsM to M′. It is shown that

Boundary regularity of correspondences in

\hat f

Hyperbolic automorphisms and holomorphic motions in C2

must extend acrossM as a locally proper holomorphic correspondence. This is a version for correspondences of the Diederich-Pinchuk extension result for CR maps.

Boundary regularity of correspondences in

We prove that the group of continuous isometries for the Kobayashi or Carathéodory metrics of a strongly convex domain in ℂ n is compact unless the domain is biholomorphic to the ball. A key ingredient, proved using differential geometric ideas, is that a continuous isometry between a strongly convex domain and the ball has to be biholomorphic or anti-biholomorphic. Combining this with a metric version of Pinchuks rescaling technique gives the main result.