SPHERES IN THE SHILOV BOUNDARIES OF BOUNDED SYMMETRIC DOMAINS
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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.
Abstract
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.
참고문헌 (16)
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