A Note on Infinite Type Germs of a Real Hypersurface in
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Abstract
Abstract: The purpose of this article is to show that there exists a smooth real hypersurface germ of D'Angelo infinite type in such that it does not admit any (singular) holomorphic curve that has infinite order contact with at .
2010 Mathematics Subject Classification. Primary 32T25; Secondary 32C25.
Key words and phrases: Holomorphic vector field, automorphism group, real hypersurface, infinite type point.
References
[1] J. P. D'Angelo, Real hypersurfaces, orders of contact, and applications, Ann. of Math. 115 (1982) 615-637.
[2] D. Catlin, Necessary conditions for subellipticity of the -Neumann problem, Ann. of Math. 117 (1) (1983) 147-171.
[3] D. Catlin, Boundary invariants of pseudoconvex domains, Ann. of Math. 120 (3) (1984) 529-586.
[4] D. Catlin, Subelliptic estimates for the -Neumann problem on pseudoconvex domains, Ann. of Math. 126 (1) (1987) 131-191.
[5] J.P. D'Angelo, Several complex variables and the geometry of real hypersurfaces, CRC Press, Boca Raton, 1993.
[6] L.Lempert, On the boundary regularity of biholomorphic mappings, Contributions to several complex variables, Aspects Math. E9 (1986) 193-215.
[7] J.E. Fornaess, L. Lee, Y. Zhang, Formal complex curves in real smooth hypersurfaces, Illinois J. Math. 58 (1) (2014) 1-10.
[8] J.E. Fornaess, B. Stensones, Infinite type germs of real analytic pseudoconvex domains in , Complex Var. Elliptic Equ. 57 (6) (2012) 705-717.
[9] K.T. Kim, V.T. Ninh, On the tangential holomorphic vector fields vanishing at an infinite type point, Trans. Amer. Math. Soc. 367(2) (2015) 867-885
References
[1] J. P. D'Angelo, Real hypersurfaces, orders of contact, and applications, Ann. of Math. 115 (1982) 615-637.
[2] D. Catlin, Necessary conditions for subellipticity of the -Neumann problem, Ann. of Math. 117 (1) (1983) 147-171.
[3] D. Catlin, Boundary invariants of pseudoconvex domains, Ann. of Math. 120 (3) (1984) 529-586.
[4] D. Catlin, Subelliptic estimates for the -Neumann problem on pseudoconvex domains, Ann. of Math. 126 (1) (1987) 131-191.
[5] J.P. D'Angelo, Several complex variables and the geometry of real hypersurfaces, CRC Press, Boca Raton, 1993.
[6] L.Lempert, On the boundary regularity of biholomorphic mappings, Contributions to several complex variables, Aspects Math. E9 (1986) 193-215.
[7] J.E. Fornaess, L. Lee, Y. Zhang, Formal complex curves in real smooth hypersurfaces, Illinois J. Math. 58 (1) (2014) 1-10.
[8] J.E. Fornaess, B. Stensones, Infinite type germs of real analytic pseudoconvex domains in , Complex Var. Elliptic Equ. 57 (6) (2012) 705-717.
[9] K.T. Kim, V.T. Ninh, On the tangential holomorphic vector fields vanishing at an infinite type point, Trans. Amer. Math. Soc. 367(2) (2015) 867-885