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On the maximum conjecture

  • Masoud Sabzevari EMAIL logo
Published/Copyright: August 7, 2018

Abstract

We verify the maximum conjecture on the rigidity of totally nondegenerate model CR manifolds in the following two cases: (i) for all models of CR dimension one, (ii) for the so-called full-models, namely those in which their associated symbol algebras are free CR. In particular, we discover that in each arbitrary CR dimension and length 3, there exists at least one totally nondegenerate model, enjoying this conjecture. Our proofs rely upon some recent results in the Tanaka theory of transitive prolongation of fundamental algebras.

MSC 2010: 32V40; 22F50

Communicated by Karl-Hermann Neeb


Award Identifier / Grant number: 96510425

Funding statement: The research of the author was supported in part by the grant from IPM, no. 96510425.

Acknowledgements

The author gratefully thanks the referee for the helpful suggestions concerning the presentation of this paper.

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Received: 2017-09-13
Revised: 2018-07-04
Published Online: 2018-08-07
Published in Print: 2018-11-01

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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