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Cartan-Chern-Moser theory on algebraic hypersurfaces and an application to the study of automorphism groups of algebraic domains

Xiaojun Huang, Shanyu Ji (2002)

Annales de l’institut Fourier

For a strongly pseudoconvex domain D n + 1 defined by a real polynomial of degree k 0 , we prove that the Lie group Aut ( D ) can be identified with a constructible Nash algebraic smooth variety in the CR structure bundle Y of D , and that the sum of its Betti numbers is bounded by a certain constant C n , k 0 depending only on n and k 0 . In case D is simply connected, we further give an explicit but quite rough bound in terms of the dimension and the degree of the defining polynomial. Our approach is to adapt the Cartan-Chern-Moser...

Certain partial differential subordinations on some Reinhardt domains in n

Gabriela Kohr, Mirela Kohr (1997)

Annales Polonici Mathematici

We obtain an extension of Jack-Miller-Mocanu’s Lemma for holomorphic mappings defined in some Reinhardt domains in n . Using this result we consider first and second order partial differential subordinations for holomorphic mappings defined on the Reinhardt domain B 2 p with p ≥ 1.

Continuity and convergence properties of extremal interpolating disks.

Pascal J. Thomas (1995)

Publicacions Matemàtiques

Let a be a sequence of points in the unit ball of Cn. Eric Amar and the author have introduced the nonnegative quantity ρ(a) = infα infk Πj:j≠k dG(αj, αk), where dG is the Gleason distance in the unit disk and the first infimum is taken over all sequences α in the unit disk which map to a by a map from the disk to the ball.The value of ρ(a) is related to whether a is an interpolating sequence with respect to analytic disks passing through it, and if a is an interpolating sequence in the ball, then...

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