{"id":23,"date":"2017-10-10T15:17:24","date_gmt":"2017-10-10T19:17:24","guid":{"rendered":"http:\/\/sites.nd.edu\/meichi\/?page_id=23"},"modified":"2025-07-29T10:25:48","modified_gmt":"2025-07-29T14:25:48","slug":"preprints","status":"publish","type":"page","link":"https:\/\/sites.nd.edu\/meichi\/preprints\/","title":{"rendered":"Recent Papers"},"content":{"rendered":"

Recent Re\/Preprints:<\/h3>\n
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  1. The Cauchy-Riemann equations on product domains. Debraj Chakrabarti and Mei-Chi Shaw, (Math. Ann. 2011)<\/a><\/li>\n
  2. L^2 Serre Duality on Domains in Complex Manifolds and Applications” by Debraj Chakrabarti and Mei-Chi Shaw (Trans. Amer. Math. Society, 2012).<\/a><\/li>\n
  3. “Duality between Harmonic and Bergman spaces” (Contemporary Mathematics, 2011).<\/a><\/li>\n
  4. “On the Hausdorff property of some Dolbeault cohomolgy groups” by Christine Laurent-Thi\\’ebaut and Mei-Chi Shaw (Math. Zeit, 2013)<\/a><\/li>\n
  5. Sobolev Regularity of the $\\overline\\partial$-equation on the Hartogs triangle. (Debraj Chakrabarti and Mei-Chi Shaw, (Math. Ann. 2013)<\/a><\/li>\n
  6. The $\\overline\\partial$-equation on an annulus with mixed boundary conditions Xiaoshan Li and Mei-Chi Shaw, (Bulletin Academia Sinica, 2013)<\/a><\/li>\n
  7. Topology of Dolbeault cohomology groups, Dedicated to Duong H. Phong (Contemporary\u00a0 Math. 2015)<\/a><\/li>\n
  8. The Hartogs Traingle in Complex Analysis (Contemporary Mathematics, 2015)<\/a><\/li>\n
  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)<\/a><\/li>\n
  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)<\/a><\/li>\n
  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)<\/a><\/li>\n
  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)<\/a><\/li>\n
  13. “On the $L^2$-Dolbeault Cohomology of Annuli” (by Debraj Chakrabarti, Christine Laurent-Thi\u00e9baut, and Mei-Chi Shaw) (Indiana University Math J., 2018)<\/a><\/li>\n
  14. Bounded plurisubharmonic\u00a0 exhaustion functions and Levi-flat hypersurfaces Siqi Fu and Mei-Chi Shaw, Dedicated to the memory of Lu Qikeng (Acta Math. Sinica, 2018)<\/a><\/li>\n
  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)<\/a><\/li>\n
  16. Holomorphic approximation via Dolbeault cohomology (by Christine Laurent-Thiebaut and Mei-Chi Shaw), Math. Zeit 2020.<\/a><\/li>\n
  17. Holomorphic approximation and mixed boundary value problems \u00a0for $\\overline\\partial$ (by Christine Laurent-Thi\\’ebaut and Mei-chi Shaw, to appear in Proc. Amer. Math. Soc.)<\/a><\/li>\n
  18. \n
    Extendability and the $\\bar\\partial$ operator on the Hartogs triangle (by A. Burchard, J. Flynn, G. Lu and M.-C. Shaw) (Math. Zeit 2022.)<\/a><\/div>\n<\/li>\n
  19. \n
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    Estimates for $\\bar\\partial$\u00a0 on domains in $C^n$ and $CP^n$, Journal\u00a0of Geometric Analysis, 2003 with the attached paper “Sibony Issue 2023”<\/a><\/div>\n<\/div>\n<\/li>\n
  20. \n
    L^2-SOBOLEV THEORY FOR \u2202 ON DOMAINS IN CP^n (to appear in the special issue in honor of Joseph J. Kohn in the J. Geometric Analysis)<\/a><\/div>\n<\/li>\n<\/ol>\n
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    HOME | My Departmental Web Site | Department of Mathematics | University of Notre Dame<\/h6>\n","protected":false},"excerpt":{"rendered":"

    Recent Re\/Preprints: The Cauchy-Riemann equations on product domains. Debraj Chakrabarti and Mei-Chi Shaw, (Math. Ann. 2011) L^2 Serre Duality on Domains in Complex Manifolds and Applications” by Debraj Chakrabarti and Mei-Chi Shaw (Trans. Amer. Math. Society, 2012). “Duality between Harmonic and Bergman spaces” (Contemporary Mathematics, 2011). “On the Hausdorff property of some Dolbeault cohomolgy groups” […]<\/p>\n","protected":false},"author":2271,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-23","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.nd.edu\/meichi\/wp-json\/wp\/v2\/pages\/23","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.nd.edu\/meichi\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.nd.edu\/meichi\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/meichi\/wp-json\/wp\/v2\/users\/2271"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/meichi\/wp-json\/wp\/v2\/comments?post=23"}],"version-history":[{"count":32,"href":"https:\/\/sites.nd.edu\/meichi\/wp-json\/wp\/v2\/pages\/23\/revisions"}],"predecessor-version":[{"id":467,"href":"https:\/\/sites.nd.edu\/meichi\/wp-json\/wp\/v2\/pages\/23\/revisions\/467"}],"wp:attachment":[{"href":"https:\/\/sites.nd.edu\/meichi\/wp-json\/wp\/v2\/media?parent=23"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}