2017/12/29 by Andrew Zimmer, Zimmer, Andrew
Mathematics · #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1712.10249
openalex publication_date 2017/12/29 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
For bounded pseudoconvex domains with finite type we give a precise\ndescription of the automorphism group: if an orbit of the automorphism group\naccumulates on at least two different points of the boundary, then the\nautomorphism group has finitely many components and is the almost direct\nproduct of a compact group and connected Lie group locally isomorphic to rm\nAut( mathbbBk). Further, the limit set is a smooth submanifold\ndiffeomorphic to the sphere of dimension 2k-1. As applications we prove a new\nfinite jet determination theorem and a Tits alternative theorem. The geometry\nof the Kobayashi metric plays an important role in the paper.\n