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A short proof of the Dimension Conjecture for real hypersurfaces in $ \mathbb{C}^2$


Authors: Alexander Isaev and Boris Kruglikov
Journal: Proc. Amer. Math. Soc. 144 (2016), 4395-4399
MSC (2010): Primary 32C05, 32V40
DOI: https://doi.org/10.1090/proc/13070
Published electronically: April 19, 2016
MathSciNet review: 3531189
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Abstract: Recently, I. Kossovskiy and R. Shafikov settled the so-called Dimension Conjecture, which characterizes spherical hypersurfaces in $ \mathbb{C}^2$ via the dimension of the algebra of infinitesimal CR-automorphisms. In this note, we propose a short argument for obtaining their result.


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Additional Information

Alexander Isaev
Affiliation: Mathematical Sciences Institute, Australian National University, Acton, Australian Capital Territory 2601, Australia
Email: alexander.isaev@anu.edu.au

Boris Kruglikov
Affiliation: Department of Mathematics and Statistics, University of Tromsø, Tromsø 90-37, Norway
Email: boris.kruglikov@uit.no

DOI: https://doi.org/10.1090/proc/13070
Keywords: Real hypersurfaces in complex space, Lie algebras of infinitesimal CR-automorphisms.
Received by editor(s): October 8, 2015
Received by editor(s) in revised form: December 20, 2015
Published electronically: April 19, 2016
Additional Notes: The first author was supported by the Australian Research Council
Communicated by: Franc Forstneric
Article copyright: © Copyright 2016 American Mathematical Society

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