Local holomorphic curves on a bounded symmetric domain in its Harish-Chandra realization exiting at regular points of the boundary

We examine the asymptotic behavior of holomorphic curves on bounded symmetric domains in their Harish-Chandra realizations exiting at smooth points of the boundary, showing that such a holomorphic curve is aysmptotically totally geodesic at a generic point of its boundary and that furthermore the norm of the second fundamental form is bounded by a constant multiple of the Euclidean distance to the boundary.

Keywords

bounded symmetric domain, Harish-Chandra realization, second fundamental form, minimal disk, minimal rational tangent, maximal polydisk

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Published 7 October 2014