[Une approche géométrique aux systèmes bord de Catlin]
Soit
qui, avec le tenseur d’ordre
Si, de plus, on suppose que
On introduit également pour
Tout récemment, la construction de
Enfin, on fait le lien entre ces invariants définis plus haut et le type fini au sens de D’Angelo, le multitype au sens de Catlin et les « boundary systems » de Catlin.
For a point
which together with Ebenfelt’s
Next, in addition, assume
and for every
Most recently, the constructions of
Finally, we relate the introduced invariants with D’Angelo’s finite type, Catlin’s multitype and Catlin’s boundary systems.
Accepté le :
Publié le :
Keywords: Catlin multitype, subelliptic estimates, boundary systems, Levi form, pseudoconvexity, real hypersurfaces, invariant tensors, ideal sheaves
Mots-clés : multitype de Catlin, estimée sous-elliptique, système bord, forme de Levi, pseudo-convexité, hypersurface réelle, tenseur invariant, faisceau idéal
Zaitsev, Dmitri 1

@article{AIF_2019__69_6_2635_0, author = {Zaitsev, Dmitri}, title = {A geometric approach to {Catlin{\textquoteright}s} boundary systems}, journal = {Annales de l'Institut Fourier}, pages = {2635--2679}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {69}, number = {6}, year = {2019}, doi = {10.5802/aif.3304}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3304/} }
TY - JOUR AU - Zaitsev, Dmitri TI - A geometric approach to Catlin’s boundary systems JO - Annales de l'Institut Fourier PY - 2019 SP - 2635 EP - 2679 VL - 69 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3304/ DO - 10.5802/aif.3304 LA - en ID - AIF_2019__69_6_2635_0 ER -
%0 Journal Article %A Zaitsev, Dmitri %T A geometric approach to Catlin’s boundary systems %J Annales de l'Institut Fourier %D 2019 %P 2635-2679 %V 69 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3304/ %R 10.5802/aif.3304 %G en %F AIF_2019__69_6_2635_0
Zaitsev, Dmitri. A geometric approach to Catlin’s boundary systems. Annales de l'Institut Fourier, Tome 69 (2019) no. 6, pp. 2635-2679. doi : 10.5802/aif.3304. https://aif.centre-mersenne.org/articles/10.5802/aif.3304/
[1] Hölder regularity of the solution to the complex Monge-Ampère equation with
[2] Plurisubharmonic polynomials and bumping, Math. Z., Volume 261 (2009) no. 1, pp. 39-63 | DOI | MR | Zbl
[3]
[4] Ideals of holomorphic functions with
[5] The Szegö projection: Sobolev estimates in regular domains, Trans. Am. Math. Soc., Volume 300 (1987) no. 1, pp. 109-132 | Zbl
[6] Boundary limits of the Bergman kernel and metric, Mich. Math. J., Volume 42 (1995) no. 3, pp. 449-461 | MR | Zbl
[7] Global regularity of the
[8] Boundary invariants of pseudoconvex domains, Ann. Math., Volume 120 (1984), pp. 529-586 | DOI | MR | Zbl
[9] Subelliptic estimates for the
[10] Estimates of invariant metrics on pseudoconvex domains of dimension two, Math. Z., Volume 200 (1989) no. 3, pp. 429-466 | DOI | MR | Zbl
[11] Subelliptic estimates, Complex analysis. Several complex variables and connections with PDE theory and geometry (Trends in Mathematics), Birkhäuser/Springer, 2010, pp. 75-94 | Zbl
[12] On compactness of the
[13] Estimates for the Bergman and Szegö projections for pseudoconvex domains of finite type with locally diagonalizable Levi form, Publ. Mat., Barc., Volume 50 (2006) no. 2, pp. 413-446 | DOI | Zbl
[14] Geometry of pseudo-convex domains of finite type with locally diagonalizable Levi form and Bergman kernel, J. Math. Pures Appl., Volume 85 (2006) no. 1, pp. 71-118 | DOI | MR | Zbl
[15] Extremal bases, geometrically separated domains and applications, Algebra Anal., Volume 26 (2014) no. 1, pp. 196-269 translation in St. Petersbg. Math. J. 26 (2015), no. 1, p. 139-191 | MR | Zbl
[16] Comparison of the Bergman and Szegö kernels, Adv. Math., Volume 228 (2011) no. 4, pp. 2366-2384 | DOI | Zbl
[17] A lower bound on the Kobayashi metric near a point of finite type in
[18] Boundary behavior of the Bergman kernel function on some pseudoconvex domains in
[19] Estimates of invariant metrics on pseudoconvex domains with comparable Levi form, J. Math. Kyoto Univ., Volume 42 (2002) no. 2, pp. 337-349 | MR | Zbl
[20] Compactness in the
[21] Subelliptic estimates and failure of semicontinuity for orders of contact, Duke Math. J., Volume 47 (1980) no. 4, pp. 955-957 | MR | Zbl
[22] Real hypersurfaces, orders of contact, and applications, Ann. Math., Volume 115 (1982), pp. 615-637 | DOI | MR | Zbl
[23] Several complex variables and the geometry of real hypersurfaces, Studies in Advanced Mathematics, CRC Press, 1993 | Zbl
[24] Pseudoconvex domains of semiregular type, Contributions to complex analysis and analytic geometry (Aspects of Mathematics), Volume E26, Vieweg & Sohn, 1994, pp. 127-161 | Zbl
[25] New invariant tensors in CR structures and a normal form for real hypersurfaces at a generic Levi degeneracy, J. Differ. Geom., Volume 50 (1998) no. 2, pp. 207-247 | DOI | MR | Zbl
[26] A construction of peak functions on some finite type domains, Am. J. Math., Volume 116 (1994) no. 3, pp. 737-755 | DOI | MR | Zbl
[27] Construction of P.S.H. functions on weakly pseudoconvex domains, Duke Math. J., Volume 58 (1989) no. 3, pp. 633-655 | MR | Zbl
[28] Local biholomorphic straightening of real submanifolds, Ann. Math., Volume 106 (1977) no. 2, pp. 319-352 | DOI | MR | Zbl
[29] The
[30] Compactness in the
[31] Boundary regularity of the solution to the complex Monge-Ampère equation on pseudoconvex domains of infinite type, Math. Res. Lett., Volume 22 (2015) no. 2, pp. 467-484 | Zbl
[32] Compact and subelliptic estimates for the
[33] Property (P) and Stein neighborhood bases on
[34] Global regularity for the
[35] Boundary invariants and the closed range property for
[36] Compactness of the Neumann operator for hyperconvex domains with non-smooth B-regular boundary, Math. Ann., Volume 307 (1997) no. 1, pp. 151-168 | DOI | MR | Zbl
[37] A sufficient condition for subellipticity of the
[38] On the Bergman metric on bounded pseudoconvex domains an approach without the Neumann operator, Int. J. Math., Volume 25 (2014) no. 3, 1450025, 13 pages | MR | Zbl
[39] On local CR-transformation of Levi-degenerate group orbits in compact Hermitian symmetric spaces, J. Eur. Math. Soc., Volume 8 (2006) no. 3, pp. 465-490 | DOI | MR | Zbl
[40] Compactness estimates for
[41] Local regularity of the Bergman projection on a class of pseudoconvex domains of finite type (2014) (https://arxiv.org/abs/1406.6532)
[42] Necessary geometric and analytic conditions for general estimates in the
[43] Harmonic integrals on strongly pseudo-convex manifolds. I, Ann. Math., Volume 78 (1963), pp. 112-148 | DOI | MR | Zbl
[44] Harmonic integrals on strongly pseudo-convex manifolds. II, Ann. Math., Volume 79 (1964), pp. 450-472 | DOI | MR | Zbl
[45] Boundary behavior of
[46] Subellipticity of the
[47] The Catlin multitype and biholomorphic equivalence of models, Int. Math. Res. Not., Volume 2010 (2010) no. 18, pp. 3530-3548 | DOI | MR | Zbl
[48] Lower bounds on the Bergman metric near a point of finite type, Ann. Math., Volume 136 (1992) no. 2, pp. 339-360 | DOI | MR | Zbl
[49] Invariant metric estimates for
[50] A sufficient condition for compactness of the
[51]
[52] Estimates for the Bergman and Szegö kernels in
[53] Direct proof of termination of the Kohn algorithm in the real-analytic case (2014) (https://arxiv.org/abs/1409.0963) | Zbl
[54] Compactness of the complex Green operator on CR-manifolds of hypersurface type, Math. Ann., Volume 348 (2010) no. 1, pp. 81-117 | DOI | MR | Zbl
[55] Compactness of the complex Green operator, Math. Res. Lett., Volume 15 (2008) no. 4, pp. 761-778 | DOI | MR | Zbl
[56] Strong Stein neighbourhood bases, Complex Var. Elliptic Equ., Volume 57 (2012) no. 10, pp. 1073-1085 | DOI | MR | Zbl
[57] Multiplier ideal sheaves in complex and algebraic geometry, Sci. China, Ser. A, Volume 48 (2005), pp. 1-31 | MR | Zbl
[58] Effective termination of Kohn’s algorithm for subelliptic multipliers, Pure Appl. Math. Q., Volume 6 (2010) no. 4, pp. 1169-1241 | MR | Zbl
[59] New procedure to generate multipliers in complex Neumann problem and effective Kohn algorithm, Sci. China, Math., Volume 60 (2017) no. 6, pp. 1101-1128 | MR | Zbl
[60] Plurisubharmonic functions and subellipticity of the
[61] Aspects of the
[62] Lectures on the
[63] The complex Green operator on CR-submanifolds of
[64] The holomorphic contact geometry of a real hypersurface, Modern methods in complex analysis (Annals of Mathematics Studies), Volume 137, Princeton University Press, 1995, pp. 327-342 | MR | Zbl
[65] Peak functions on weakly pseudoconvex domains, Indiana Univ. Math. J., Volume 43 (1994) no. 4, pp. 1271-1295 | MR | Zbl
- Catlin's boundary systems for sums of squares domains, Journal of Mathematical Analysis and Applications, Volume 531 (2024) no. 1, p. 127772 | DOI:10.1016/j.jmaa.2023.127772
- Boundary invariants and the closed range property for ∂¯, Differential Geometry and its Applications, Volume 82 (2022), p. 101871 | DOI:10.1016/j.difgeo.2022.101871
- Infinitesimal symmetries of weakly pseudoconvex manifolds, Mathematische Zeitschrift, Volume 300 (2022) no. 3, p. 2451 | DOI:10.1007/s00209-021-02873-w
- Triangular resolutions and effectiveness for holomorphic subelliptic multipliers, Advances in Mathematics, Volume 387 (2021), p. 107803 | DOI:10.1016/j.aim.2021.107803
- Newton polyhedra and order of contact on real hypersurfaces, Journal of the Mathematical Society of Japan, Volume 73 (2021) no. 1 | DOI:10.2969/jmsj/80868086
Cité par 5 documents. Sources : Crossref