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On the real-analyticity of rigid spherical hypersurfaces in $ \mathbb{C}^2$


Authors: Alexander Isaev and Joël Merker
Journal: Proc. Amer. Math. Soc. 147 (2019), 5251-5256
MSC (2010): Primary 32V05, 35J46, 35J48
DOI: https://doi.org/10.1090/proc/14724
Published electronically: July 30, 2019
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Abstract: We prove that every smooth rigid spherical hypersurface in $ \mathbb{C}^2$ is in fact real-analytic. As an application of this result, it follows that the classification of real-analytic rigid spherical hypersurfaces in $ \mathbb{C}^2$ found by V. Ezhov and G. Schmalz applies in the smooth case.


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Additional Information

Joël Merker
Affiliation: Mathematical Sciences Institute, Australian National University, Canberra, Acton, ACT 2601, Australia; Laboratoire de Mathématiques d’Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay Cedex, France
Email: alexander.isaev@anu.edu.au, joel.merker@math.u-psud.fr

DOI: https://doi.org/10.1090/proc/14724
Keywords: Rigid hypersurfaces, zero CR-curvature equation, nonlinear elliptic systems, real-analyticity of solutions
Received by editor(s): March 4, 2019
Received by editor(s) in revised form: March 11, 2019
Published electronically: July 30, 2019
Communicated by: Filippo Bracci
Article copyright: © Copyright 2019 American Mathematical Society