Mappings of real algebraic hypersurfaces

Baouendi, M. S.; Rothschild, Linda Preiss

doi:10.1090/S0894-0347-1995-1317227-3

Mappings of real algebraic hypersurfaces
HTML articles powered by AMS MathViewer

by M. S. Baouendi and Linda Preiss Rothschild

J. Amer. Math. Soc. 8 (1995), 997-1015

DOI: https://doi.org/10.1090/S0894-0347-1995-1317227-3

PDF | Request permission

References

M. Artin, On the solutions of analytic equations, Invent. Math. 5 (1968), 277–291. MR 232018, DOI 10.1007/BF01389777
M. Artin, Algebraic approximation of structures over complete local rings, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 23–58. MR 268188
M. S. Baouendi, H. Jacobowitz, and F. Trèves, On the analyticity of CR mappings, Ann. of Math. (2) 122 (1985), no. 2, 365–400. MR 808223, DOI 10.2307/1971307
M. S. Baouendi and Linda Preiss Rothschild, Germs of CR maps between real analytic hypersurfaces, Invent. Math. 93 (1988), no. 3, 481–500. MR 952280, DOI 10.1007/BF01410197
M. S. Baouendi and Linda Preiss Rothschild, Geometric properties of mappings between hypersurfaces in complex space, J. Differential Geom. 31 (1990), no. 2, 473–499. MR 1037411
M. S. Baouendi and Linda Preiss Rothschild, Images of real hypersurfaces under holomorphic mappings, J. Differential Geom. 36 (1992), no. 1, 75–88. MR 1168982
Eric Bedford and Steve Bell, Extension of proper holomorphic mappings past the boundary, Manuscripta Math. 50 (1985), 1–10. MR 784136, DOI 10.1007/BF01168824
Salomon Bochner and William Ted Martin, Several Complex Variables, Princeton Mathematical Series, vol. 10, Princeton University Press, Princeton, N. J., 1948. MR 0027863
S. S. Chern and J. K. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219–271. MR 425155, DOI 10.1007/BF02392146
J. Denef and L. Lipshitz, Power series solutions of algebraic differential equations, Math. Ann. 267 (1984), no. 2, 213–238. MR 738249, DOI 10.1007/BF01579200
K. Diederich and J. E. Fornæss, Proper holomorphic mappings between real-analytic pseudoconvex domains in $\textbf {C}^n$, Math. Ann. 282 (1988), no. 4, 681–700. MR 970228, DOI 10.1007/BF01462892
K. Diederich and S. M. Webster, A reflection principle for degenerate real hypersurfaces, Duke Math. J. 47 (1980), no. 4, 835–843. MR 596117
Franc Forstnerič, Extending proper holomorphic mappings of positive codimension, Invent. Math. 95 (1989), no. 1, 31–61. MR 969413, DOI 10.1007/BF01394144
Michael Freeman, Real submanifolds with degenerate Levi form, Several complex variables (Proc. Sympos. Pure Math., Vol. XXX, Part 1, Williams Coll., Williamstown, Mass., 1975) Amer. Math. Soc., Providence, R.I., 1977, pp. 141–147. MR 0457767
Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0180696
Xiao Jun Huang, On the mapping problem for algebraic real hypersurfaces in the complex spaces of different dimensions, Ann. Inst. Fourier (Grenoble) 44 (1994), no. 2, 433–463 (English, with English and French summaries). MR 1296739
J. J. Kohn, Boundary behavior of $\delta$ on weakly pseudo-convex manifolds of dimension two, J. Differential Geometry 6 (1972), 523–542. MR 322365
Katsumi Nomizu, Lie groups and differential geometry, Mathematical Society of Japan, Tokyo, 1956. MR 0084166

Les fonctions analytiques de deux variables et la représentation conforme

23

Nancy K. Stanton, Infinitesimal CR automorphisms of rigid hypersurfaces, Amer. J. Math. 117 (1995), no. 1, 141–167. MR 1314461, DOI 10.2307/2375039
Noboru Tanaka, On the pseudo-conformal geometry of hypersurfaces of the space of $n$ complex variables, J. Math. Soc. Japan 14 (1962), 397–429. MR 145555, DOI 10.2969/jmsj/01440397
S. M. Webster, On the mapping problem for algebraic real hypersurfaces, Invent. Math. 43 (1977), no. 1, 53–68. MR 463482, DOI 10.1007/BF01390203
S. M. Webster, On mapping an $n$-ball into an $(n+1)$-ball in complex spaces, Pacific J. Math. 81 (1979), no. 1, 267–272. MR 543749