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The Dimension Conjecture: Solution and Future Prospects
M. A. Stepanova Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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.
Received: 20.05.2022 Revised: 25.06.2022
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
Linking options:
https://www.mathnet.ru/eng/mzm13458https://doi.org/10.4213/mzm13458 https://www.mathnet.ru/eng/mzm/v112/i5/p784
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Abstract page: | 243 | Full-text PDF : | 26 | References: | 64 | First page: | 10 |
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