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# Mathematical Research Letters

## Volume 22 (2015)

### Number 4

### Deformations of CR manifolds, parametrizations of automorphisms, and applications

Pages: 1089 – 1127

DOI: http://dx.doi.org/10.4310/MRL.2015.v22.n4.a7

#### Authors

#### Abstract

We prove a parametrization theorem for maps of deformations of minimal, holomorphically nondegenerate real-analytic CR manifolds. This is used to deduce results on biholomorphic equivalence; we show that one can, for any germ of a minimal, holomorphically nondegenerate real-analytic CR manifold $(M,p)$ construct a function which completely characterizes the CR manifolds biholomorphically equivalent to $(M,p)$. As an application, we show that for any $p \in M$, the equivalence locus $E_p = \{ q \in M : (M,q)$ biholomorphically equivalent to $(M,p) \}$ is a locally closed real-analytic submanifold of $M$, and give a criterion for the global CR automorphism group to be a (finite-dimensional) Lie group.

#### 2010 Mathematics Subject Classification

32H02, 32V40