On the intersection of varieties with a totally real submanifold
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- by Howard Jacobowitz PDF
- Proc. Amer. Math. Soc. 101 (1987), 127-130 Request permission
Abstract:
In their work on uniqueness in the Cauchy problem for CR functions, Baouendi and Treves have utilized a condition on a totally real submanifold $M$ in a neighborhood of one of its points $p$: There should exist a variety $X$ such that the component containing $p$ of $M - \left ( {M \cap X} \right )$ has compact closure in $M$. All real analytic submanifolds satisfy this condition. In this paper, a ${C^\infty }$ submanifold is constructed which does not. Uniqueness in the corresponding Cauchy problem remains unresolved.References
- M. S. Baouendi and F. Trèves, Unique continuation in CR manifolds and in hypo-analytic structures, Ark. Mat. 26 (1988), no. 1, 21–40. MR 948278, DOI 10.1007/BF02386106
- Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0180696
- Robert M. Hardt, Slicing and intersection theory for chains associated with real analytic varieties, Acta Math. 129 (1972), 75–136. MR 315561, DOI 10.1007/BF02392214
- Hassler Whitney, Complex analytic varieties, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1972. MR 0387634
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 101 (1987), 127-130
- MSC: Primary 32F25
- DOI: https://doi.org/10.1090/S0002-9939-1987-0897082-3
- MathSciNet review: 897082