# Papers and Talks

## Papers

[11] (with J. Brinkschulte) Dynamical aspects of foliations with ample normal bundle
Preprint. arXiv:2105.10226.
[10] (with S. Biard) On Levi flat hypersurfaces with transversely affine foliation
Preprint. arXiv:2011.06379.
[9] (with J. Yum) Diederich–Fornæss and Steinness indices for abstract CR manifolds
J. Geom. Anal., published online, 2021.
DOI:10.1007/s12220-020-00598-6. arXiv:2003.01330.
[8] On a hyperconvex manifold without non-constant bounded holomorphic functions
Geometric Complex Analysis, 1–10, Springer Proc. Math. Stat., 246, Springer, Singapore, 2018.
DOI:10.1007/978-981-13-1672-2_1. arXiv:1804.09569.
In page 3, the uniqueness statement in Fact 2 was not stated correctly. The complex structure on $X$ satisfying three conditions is not uniquely determined, although their biholomorphism type is uniquely determined.
Some other minor inaccuracies remain in the arXiv version, which are fixed in the published version.
[7] On weighted Bergman spaces of a domain with Levi-flat boundary
Trans. Amer. Math. Soc. 374 (2021), 7499–7524.
DOI:10.1090/tran/8471. arXiv:1703.08165.
The title was changed from “Weighted Bergman spaces of domains with Levi-flat boundary: geodesic segments on compact Riemann surfaces”.
[6] A CR proof for a global estimate of the Diederich–Fornaess index of Levi-flat real hypersurfaces
Complex Analysis and Geometry, 41–48, Springer Proc. Math. Stat., 144, Springer, Tokyo, 2015.
DOI:10.1007/978-4-431-55744-9_2. arXiv:1410.2789.
In page 46, line 7, the mysterious citation should read [BI].
[5] (with J. Brinkschulte) Curvature restrictions for Levi-flat real hypersurfaces in complex projective planes
Ann. Inst. Fourier (Grenoble) 65 (2015), no. 6, 2547–2569.
DOI:10.5802/aif.2995. arXiv:1410.2695.
[4] On a global estimate of the Diederich–Fornaess index of Levi-flat real hypersurfaces
Geometry, Dynamics, and Foliations 2013, 259–268, Adv. Stud. Pure Math., 72, Math. Soc. Japan, Tokyo, 2017.
DOI:10.2969/aspm/07210259 arXiv:1410.2693.
[3] (with J. Brinkschulte) A global estimate for the Diederich–Fornaess index of weakly pseudoconvex domains
Nagoya Math. J. 220 (2015), 67–80.
DOI:10.1215/00277630-3335655. arXiv:1401.2264.
[2] A local expression of the Diederich–Fornaess exponent and the exponent of conformal harmonic measures
Bull. Braz. Math. Soc. (N.S.) 46 (2015), no. 1, 65–79.
DOI:10.1007/s00574-015-0084-z. arXiv:1403.3179.
In page 67, Theorem 2.4 was not stated correctly. We had stated it as "if and only if" statement. What follows from Ohsawa-Sibony’s Theorem is its "if" part. We do not know whether "only if" part holds. This affects other part of this paper, and we need to correct the following statements:

• Theorem 1.1, Corollary 1.2 needs an extra assumption that the normal bundle admits a hermitian metric of positive curvature.
• In Theorem 3.2, Proposition 3.3, the condition "with positive Diederich-Fornaess exponent" should read "with strong Oka property".
• In Page 74, line 12, the strict inequality follows from the extra assumption, not from Proposition 3.3.

Further discussion on this error can be found in [9].

In page 76, line 7, "flat CR line bundle" should read "leafwise flat CR line bundle". The structure group mentioned there should be understood as that of line bundles restricted on each leaf.
[1] On the ampleness of positive CR line bundles over Levi-flat manifolds
Publ. Res. Inst. Math. Sci. 50 (2014), no. 1, 153–167.
DOI:10.4171/PRIMS/127. arXiv:1301.5957.
In page 157, line 6, "an anti-biholomorphism" should read "anti-biholomorphic in $\zeta$"; the conjugation map is not anti-holomorphic in $z$ but is holomorphic in $z$.
In page 160, line 4, the definition of $r$ should read $r = r_0 e^{-\psi \circ \pi}$; $\psi$ defined on the base Riemann surface was implicitly identified with $\psi \circ \pi$ defined on the ruled surface.
In page 164, line 20, $\min$ should read $\max$.
In page 164, line 21, the reasoning to show the lower estimate for RHS does not make sense. We should modify the definition of $N_0$ in page 162 by adding $+1$ to the original definition so that we have $i\Theta_h < -i\partial\overline{\partial}(-\log(-r))$ on $D \sqcup D’$.

## Abstracts, reports, slides and videos on my talks

Weighted Bergman spaces of domains with Levi-flat boundary
Introductory lecture about [7] and [8] at a KIAS workshop “Progress in Several Complex Variables”, April 2018.
Handwritten lecture notes are available at Progress in Several Complex Variables.

For older ones, see my old webpage at this moment.