Local polynomial convexity of the union of two totally-real surfaces at their intersection

Gorai, Sushil (2011) Local polynomial convexity of the union of two totally-real surfaces at their intersection. In: Manuscripta Mathematica, 135 (1-2). pp. 43-62.

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Abstract

We consider the following question: Let S (1) and S (2) be two smooth, totally-real surfaces in C-2 that contain the origin. If the union of their tangent planes is locally polynomially convex at the origin, then is S-1 boolean OR S-2 locally polynomially convex at the origin? If T (0) S (1) a (c) T (0) S (2) = {0}, then it is a folk result that the answer is yes. We discuss an obstruction to the presumed proof, and provide a different approach. When dim(R)(T0S1 boolean AND T0S2) = 1, we present a geometric condition under which no consistent answer to the above question exists. We then discuss conditions under which we can expect local polynomial convexity.

Item Type:	Journal Article
Publication:	Manuscripta Mathematica
Publisher:	Springer
Additional Information:	Copyright of this article belongs to Springer.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	26 Apr 2011 08:16
Last Modified:	26 Apr 2011 08:16
URI:	http://eprints.iisc.ac.in/id/eprint/37149

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