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The local polynomial hull near a degenerate CR singularity: Bishop discs revisited

Bharali, Gautam (2012) The local polynomial hull near a degenerate CR singularity: Bishop discs revisited. In: MATHEMATISCHE ZEITSCHRIFT, 271 (3-4). pp. 1043-1063.

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Official URL: http://dx.doi.org/10.1007/s00209-011-0902-y


Let be a smooth real surface in and let be a point at which the tangent plane is a complex line. How does one determine whether or not is locally polynomially convex at such a p-i.e. at a CR singularity? Even when the order of contact of with at p equals 2, no clean characterisation exists; difficulties are posed by parabolic points. Hence, we study non-parabolic CR singularities. We show that the presence or absence of Bishop discs around certain non-parabolic CR singularities is completely determined by a Maslov-type index. This result subsumes all known facts about Bishop discs around order-two, non-parabolic CR singularities. Sufficient conditions for Bishop discs have earlier been investigated at CR singularities having high order of contact with . These results relied upon a subharmonicity condition, which fails in many simple cases. Hence, we look beyond potential theory and refine certain ideas going back to Bishop.

Item Type: Journal Article
Additional Information: Copyright for this article belongs Springer
Keywords: Bishop disc; Complex tangency; CR singularity; Polynomially convex
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Francis Jayakanth
Date Deposited: 17 Aug 2012 06:51
Last Modified: 17 Aug 2012 06:51
URI: http://eprints.iisc.ac.in/id/eprint/44939

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