2004
DOI: 10.1007/s00209-004-0711-7
|View full text |Cite
|
Sign up to set email alerts
|

Estimates for the -Neumann problem and nonexistence of C2 Levi-flat hypersurfaces in

Abstract: We would like to thank Professors T. Ohsawa and K. Diederich for pointing out an error in our paper [CSW]. The inequality (4.18) in the proof of Proposition 4.5 is not valid. Step 2 in the proof of Proposition 4.5 should be changed to the following stronger statement using the unweighted∂-Neumann operator. Proposition 4.5 still holds after the correction with other steps unchanged.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1
1

Citation Types

1
20
0
2

Year Published

2005
2005
2024
2024

Publication Types

Select...
4
1

Relationship

1
4

Authors

Journals

citations
Cited by 23 publications
(23 citation statements)
references
References 2 publications
1
20
0
2
Order By: Relevance
“…In [4], we carried out an L 2 approach for∂-closed extension problem using thē ∂-Neumann operator in order to study the nonexistence of C 2 -smooth Levi-flat real hypersurfaces in CP n . In fact, only the nonexistence of C 2,α Levi-flat hypersurfaces in CP n with n ≥ 3 was proved, by using∂-closed extension of the Chern connection (0, 1)-forms (see Sect.…”
Section: Definition a Lipschitz Hypersurface Is A Hypersurface Which mentioning
confidence: 99%
See 2 more Smart Citations
“…In [4], we carried out an L 2 approach for∂-closed extension problem using thē ∂-Neumann operator in order to study the nonexistence of C 2 -smooth Levi-flat real hypersurfaces in CP n . In fact, only the nonexistence of C 2,α Levi-flat hypersurfaces in CP n with n ≥ 3 was proved, by using∂-closed extension of the Chern connection (0, 1)-forms (see Sect.…”
Section: Definition a Lipschitz Hypersurface Is A Hypersurface Which mentioning
confidence: 99%
“…In fact, only the nonexistence of C 2,α Levi-flat hypersurfaces in CP n with n ≥ 3 was proved, by using∂-closed extension of the Chern connection (0, 1)-forms (see Sect. 5 in [4]). The proof for the CP 2 case in Sect.…”
Section: Definition a Lipschitz Hypersurface Is A Hypersurface Which mentioning
confidence: 99%
See 1 more Smart Citation
“…Note that (6) and (9) give us natural bounds for the complex hessian of − log(−ρ). For future reference, we observe that (8) is equivalent to:…”
Section: Local Properties Of Pseudoconvex Domainsmentioning
confidence: 99%
“…On C 2 domains, we may use a result of Diederich and Fornaess [15] that allows us to construct a global defining function ρ so that −(−ρ) η is a bounded plurisubharmonic function for some 0 < η < 1. In [3], Berndtsson and Charpentier show that in such cases the Bergman projection and the canonical solution operator ∂ * N are regular in any Sobolev space W s , 0 ≤ s < η 2 (see also [6]). However, in [14] Diederich and Fornaess use worm domains to show that for any 0 < η < 1, one can find a smooth pseudoconvex domain where −(−ρ) η is not plurisubharmonic for any global defining function ρ.…”
Section: Introductionmentioning
confidence: 99%