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We prove that a class of perturbations of standard $\text{CR}$ structure on the boundary of threedimensional complex ellipsoid ${{E}_{p,\,q}}$ can be realized as hypersurfaces on ${{\mathbb{C}}^{2}}$, which generalizes the result of Burns and Epstein on the embeddability of some perturbations of standard $\text{CR}$ structure on ${{S}^{3}}$.

Let W be the usual almost-sure limit random variable in a supercritical simple branching process; we study its tail behaviour. For the left tail, we distinguish two cases, the ‘Schröder' and ‘Böttcher' cases; both appear in work of Harris and Dubuc. The Schröder case is related to work of Karlin and McGregor on embeddability in continuous-time (Markov) branching processes. New results are obtained for the Böttcher case; there are links with recent work of Barlow and Perkins on Brownian motion on a fractal. The right tail is also considered. Use is made of recent progress in Tauberian theory.

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Embeddability of Some Three-Dimensional Weakly Pseudoconvex $\text{CR}$ Structures

On the limit of a supercritical branching process

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Embeddability of Some Three-Dimensional Weakly Pseudoconvex $\text{CR}$ Structures

On the limit of a supercritical branching process