NDLI: Tangent discs and extension ofCR functions to wedges of ℂ$^{ n }$

Content Provider	Springer Nature Link
Author	Baracco, Luca Zampieri, Giuseppe
Copyright Year	2002
Abstract	Let V be a “wedge” with “generic” edge N in a submanifold M ofX = ℂ$^{ n }$. We treat the problem whether a C R function on V which extends at some point p$_{1}$∈V to some direction normal to M, also extends at a point p$_{o}$∈ N to some direction normal to N and transversal to M (related to the former). We give positive answer to the above question when there exists a small analytic disc “attached to V ∪ N” and containing p$_{o}$ and p$_{1}$ in its boundary. In case the disc is tangent to M at p$_{o}$ the relation between the initial direction of extendibility and the new one is very tight. This is related to, but somewhat more general than the conclusion by Tumanov [7] where “propagators of extendibility” are a particular family of “tangent discs” that is the projection on X of analytic discs attached to a special subbundle E$^{}$ of T$_{M}$ $^{}$X and the directions of extension are those of E. Let us also quote [9] for a full geometric description of propagation of extendibility for CR functions on manifolds (instead of wedges). As a corollary of our result, we regain Tumanov statement on extension to “full dimensional” wedges with edge N for holomorphic functions in a neighborhood of V. However, our proof is much simpler and especially does not use the full strength of Tumanov theory of wedge extension under “minimality”.
Starting Page	1
Ending Page	7
Page Count	7
File Format	PDF
ISSN	10506926
Journal	Journal of Geometric Analysis
Volume Number	12
Issue Number	1
e-ISSN	1559002X
Language	English
Publisher	Springer-Verlag
Publisher Date	2002-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	CR functions analytic discs Continuation of analytic objects Differential Geometry Convex and Discrete Geometry Fourier Analysis Abstract Harmonic Analysis Dynamical Systems and Ergodic Theory Global Analysis and Analysis on Manifolds
Content Type	Text
Resource Type	Article
Subject	Geometry and Topology

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