On an -manifold in

near an elliptic complex tangent

Author:
Xiaojun Huang

Journal:
J. Amer. Math. Soc. **11** (1998), 669-692

MSC (1991):
Primary 32F25, 32D05

MathSciNet review:
1603854

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we study the local biholomorphic property of a real -manifold near an elliptic complex tangent point . In particular, we are interested in the regularity and the unique disk-filling problem of the local hull of holomorphy of near , first considered in a paper of Bishop. When is a -smooth submanifold, using a result established by Kenig-Webster, we show that near , is a smooth Levi-flat -manifold with a neighborhood of in as part of its boundary. Moreover, near , is foliated by a family of disjoint embedded complex analytic disks. We also prove a uniqueness theorem for the analytic disks attached to . This result was proved in the previous work of Kenig-Webster when . When is real analytic, we show that is real analytic with a neighborhood of in as part of its real analytic boundary. Equivalently, we prove the convergence of the formal solutions of a certain functional equation. When or when but the Bishop invariant does not vanish at the point under study, the analyticity was then previously obtained in the work of Moser-Webster, Moser, and in the author's joint work with Krantz.

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Additional Information

**Xiaojun Huang**

Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903

Email:
huangx@math.rutgers.edu

DOI:
https://doi.org/10.1090/S0894-0347-98-00265-3

Received by editor(s):
August 8, 1997

Received by editor(s) in revised form:
February 9, 1998

Additional Notes:
The author was supported in part by NSF DMS-9500881 and an NSF postdoctoral fellowship

Article copyright:
© Copyright 1998
American Mathematical Society