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Matematicheskie Zametki, 2022, Volume 112, Issue 5, Pages 784–800
DOI: https://doi.org/10.4213/mzm13458
(Mi mzm13458)
 

The Dimension Conjecture: Solution and Future Prospects

M. A. Stepanova

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
References:
Abstract: Counterexamples to the dimension conjecture in CR geometry are constructed. This conjecture is organically related to the model surface method; it was refined as the method was developed. On the one hand, these counterexamples give a final negative solution of the conjecture in its original setting. On the other hand, they make it possible to distinguish a natural class of manifolds (nondegenerate manifolds) for which the conjecture makes sense and is of interest. The main questions arising in this direction are formulated. A series of examples interesting from the point of view of the model surface method are considered.
Keywords: CR manifold, automorphism, Bloom–Graham type.
Funding agency Grant number
Russian Science Foundation 19-11-00316
This work was supported by the Russian Science Foundation, project no. 19-11-00316.
Received: 20.05.2022
Revised: 25.06.2022
English version:
Mathematical Notes, 2022, Volume 112, Issue 5, Pages 776–788
DOI: https://doi.org/10.1134/S000143462211013X
Bibliographic databases:
Document Type: Article
UDC: 517.55
Language: Russian
Citation: M. A. Stepanova, “The Dimension Conjecture: Solution and Future Prospects”, Mat. Zametki, 112:5 (2022), 784–800; Math. Notes, 112:5 (2022), 776–788
Citation in format AMSBIB
\Bibitem{Ste22}
\by M.~A.~Stepanova
\paper The Dimension Conjecture: Solution and Future Prospects
\jour Mat. Zametki
\yr 2022
\vol 112
\issue 5
\pages 784--800
\mathnet{http://mi.mathnet.ru/mzm13458}
\crossref{https://doi.org/10.4213/mzm13458}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4538805}
\transl
\jour Math. Notes
\yr 2022
\vol 112
\issue 5
\pages 776--788
\crossref{https://doi.org/10.1134/S000143462211013X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85145391149}
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