| Let D,D' be bounded domains in C2 having smooth, real analytic boundaries and f&d4;: D→D' a proper holomorphic correspondence. It is shown that f&d4; extends as a correspondence across 6D . The idea is to first show that f&d4; extends across an open dense set of 6D . The Segre correspondence can be constructed by combining this with the reflection principle and this is used to extend f&d4; across the remaining boundary points.;We also obtain a version of the Schwarz lemma for correspondences f&d4;: D→D where D⊂C is the unit disc and D⊂⊂Cn is a domain whose each boundary point is a local plurisubharmonic peak point. This is used to show the 'non-increasing' property of the Kobayashi metric in strictly pseudoconvex domains for holomorphic correspondences. |
