SPHERES IN THE SHILOV BOUNDARIES OF BOUNDED SYMMETRIC DOMAINS

초록

In this paper, we classify all nonconstant smooth CR maps from a sphere Sn,1 ⊂ ℂ^n with n>3 to the Shilov boundary S_(p,q) ⊂ ℂ_(p×q) of a bounded symmetric domain of Cartan type I under the condition that p-q<3n-4. We show that they are either linear maps up to automorphisms of S_(n,1) and S_(p,q) or D'Angelo maps. This is the first classification of CR maps into the Shilov boundary of bounded symmetric domains other than sphere that includes nonlinearmaps.

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