Recent Papers

Recent Re/Preprints:

1. The Cauchy-Riemann equations on product domains. Debraj Chakrabarti and Mei-Chi Shaw, (Math. Ann. 2011)
2. L^2 Serre Duality on Domains in Complex Manifolds and Applications” by Debraj Chakrabarti and Mei-Chi Shaw (Trans. Amer. Math. Society, 2012).
3. “Duality between Harmonic and Bergman spaces” (Contemporary Mathematics, 2011).
4. “On the Hausdorff property of some Dolbeault cohomolgy groups” by Christine Laurent-Thi\’ebaut and Mei-Chi Shaw (Math. Zeit, 2013)
5. Sobolev Regularity of the $\overline\partial$-equation on the Hartogs triangle. (Debraj Chakrabarti and Mei-Chi Shaw, (Math. Ann. 2013)
6. The $\overline\partial$-equation on an annulus with mixed boundary conditions Xiaoshan Li and Mei-Chi Shaw, (Bulletin Academia Sinica, 2013)
7. Topology of Dolbeault cohomology groups, Dedicated to Duong H. Phong (Contemporary  Math. 2015)
8. The Hartogs Traingle in Complex Analysis (Contemporary Mathematics, 2015)
9. “The $L^2$-cohomology of a bounded smooth Stein Domain is not necessarily Hausdorff” by Debraj Chakrabarti and Mei-Chi Shaw (Math Ann., 2015)
10. Non-closed range property for the Cauchy-Riemann operator (by Christine Laurent-Thi\'{e}baut and Mei-Chi Shaw) (Proceedings of the Conference in memory of M. S. Baouendi, 2015)
11. “The Diederich-Forness exponent and non-existence of Stein domains with Levi-flat boundaries” (by Siqi Fu and Mei-Chi Shaw, 2016) (J. Geometric Analysis, 2016)
12. Hearing pseudoconvexity in Lipschitz domains with holes with $\bar\partial$, Siqi Fu, Christine Laurent-Thi\'{e}baut and Mei-Chi Shaw, (Math. Zeit, 2017)
13. “On the $L^2$-Dolbeault Cohomology of Annuli” (by Debraj Chakrabarti, Christine Laurent-Thiébaut, and Mei-Chi Shaw) (Indiana University Math J., 2018)
14. Bounded plurisubharmonic  exhaustion functions and Levi-flat hypersurfaces Siqi Fu and Mei-Chi Shaw, Dedicated to the memory of Lu Qikeng (Acta Math. Sinica, 2018)
15. Solving $\bar\partial$ with prescribed support on Hartogs triangles in $C^2$ and $CP^2$, Christine Laurent-Thi\'{e}baut and Mei-Chi Shaw, (Trans. Amer. Math. Soc., 2019)
16. Holomorphic approximation via Dolbeault cohomology (by Christine Laurent-Thiebaut and Mei-Chi Shaw), Math. Zeit 2020.
17. Holomorphic approximation and mixed boundary value problems  for $\overline\partial$ (by Christine Laurent-Thi\’ebaut and Mei-chi Shaw, to appear in Proc. Amer. Math. Soc.)
18. Extendability and the $\bar\partial$ operator on the Hartogs triangle (by A. Burchard, J. Flynn, G. Lu and M.-C. Shaw) (Math. Zeit 2022.)
19. Estimates for $\bar\partial$  on domains in $C^n$ and $CP^n$, Journal of Geometric Analysis, 2003 with the attached paper “Sibony Issue 2023”

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