10,434 research outputs found
Holonomy representations which are a diagonal direct sum of two faithful representations
We study holonomy representations admitting a pair of supplementary faithful
sub-representations. In particular the cases where the sub-representations are
isomorphic respectively dual to each other are treated. In each case we have a
closer look at the classification in small dimension
Infinitesimal semisimple symplectic extrinsic symmetric spaces
We study infinitesimal semi-simple extrinsic symmetric spaces and give a
classification in the symplectic case
Semicontinuity of the Automorphism Groups of Domains with Rough Boundary
Based on some ideas of Greene and Krantz, we study the semicontinuity of
automorphism groups of domains in one and several complex variables. We show
that semicontinuity fails for domains in \CC^n, , with Lipschitz
boundary, but it holds for domains in \CC^1 with Lipschitz boundary. Using
the same ideas, we develop some other concepts related to mappings of Lipschitz
domains. These include Bergman curvature, stability properties for the Bergman
kernel, and also some ideas about equivariant embeddings
The corona problem with two pieces of data
We study the corona problem on the unit ball in \CC^n, and more generally
on strongly pseudoconvex domains in \CC^n. When the corona problem has just
two pieces of data, and an extra geometric hypothesis is satisfied, then we are
able to solve it
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