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A global estimate for the Diederich-Fornaess index of weakly pseudoconvex domains

Published online by Cambridge University Press:  11 January 2016

Masanori Adachi
Affiliation:
Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Tokyo, [email protected]
Judith Brinkschulte
Affiliation:
Universität Leipzig, Mathematisches Institut, D-04009 Leipzig, [email protected]
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Abstract

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A uniform upper bound for the Diederich-Fornaess index is given for weakly pseudoconvex domains whose Levi form of the boundary vanishes in l-directions everywhere.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2015

References

[1] Adachi, M., On the ampleness of positive CR line bundles over Levi-flat manifolds, Publ. Res. Inst. Math. Sci. 50 (2014), 153167. MR 3167582. DOI 10.4171/PRIMS/127.Google Scholar
[2] Berndtsson, B. and Charpentier, P., A Sobolev mapping property of the Bergman kernel, Math. Z. 235 (2000), 110. MR 1785069. DOI 10.1007/s002090000099.Google Scholar
[3] Brinkschulte, J., The -problem with support conditions on some weakly pseudoconvex domains, Ark. Mat. 42 (2004), 259282. MR 2101387. DOI 10.1007/BF02385479.Google Scholar
[4] Cao, J., Shaw, M.-C., and Wang, L., Estimates for the -Neumann problem and nonexistence of C2 Levi-flat hypersurfaces ℂℙn , Math. Z. 248 (2004), 183221; Correction, Math. Z. 248 (2004), 223-225. MR 2092728; MR 2092729. DOI 10.1007/s00209-004-0661-0.Google Scholar
[5] Chakrabarti, D. and Shaw, M.-C., L2 Serre duality on domains in complex manifolds and applications, Trans. Amer. Math. Soc. 364, no. 7 (2012), 35293554. MR 2901223. DOI 10.1090/S0002-9947-2012-05511-5.Google Scholar
[6] Demailly, J.-P., Complex Analytic and Differential Geometry, preprint, https://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/agbook.pdf (accessed September 16, 2015).Google Scholar
[7] Diederich, K. and Fornaess, J. E., Pseudoconvex domains: Bounded strictly plurisub-harmonic exhaustion functions, Invent. Math. 39 (1977), 129141. MR 0437806.Google Scholar
[8] Diederich, K. and Fornaess, J. E., Pseudoconvex domains: An example with nontrivial Nebenhülle, Math. Ann. 225 (1977), 275292. MR 0430315.Google Scholar
[9] Donnelly, H. and Fefferman, C., L2-cohomology and index theorem for the Bergman metric, Ann. of Math. (2) 118 (1983), 593618. MR 0727705. DOI 10.2307/2006983.Google Scholar
[10] Fu, S. and Shaw, M.-C., The Diederich–Fornaess exponent and non-existence of Stein domains with Levi-flat boundaries, published electronically 25 November 2014. DOI 10.1007/s12220-014-9546-6.Google Scholar
[11] Harrington, P. S. and Shaw, M.-C., The strong Oka’s lemma, bounded plurisubharmonic functions and the -Neumann problem, Asian J. Math. 11 (2007), 127139. MR 2304586. DOI 10.4310/AJM.2007.v11.n1.a12.Google Scholar
[12] Ohsawa, T. and Sibony, N., Bounded p.s.h. functions and pseudoconvexity in Kähler manifolds, Nagoya Math. J. 149 (1998), 18. MR 1619572 Google Scholar