{"id":5,"date":"2020-01-10T12:15:58","date_gmt":"2020-01-10T12:15:58","guid":{"rendered":"http:\/\/sites.rutgers.edu\/professor-example\/?page_id=5"},"modified":"2026-02-12T19:57:36","modified_gmt":"2026-02-12T19:57:36","slug":"research","status":"publish","type":"page","link":"https:\/\/sites.rutgers.edu\/bin-guo\/research\/","title":{"rendered":"Research"},"content":{"rendered":"

I do research in Geometric Analysis<\/a> and Complex Differential Geometry.<\/a> Recently, I am mainly interested in the regularity theory of nonlinear partial differential equations on complex manifolds, and their applications to the geometry of K\u00e4hler metrics.<\/p>\n

Publications (in peer-reviewed journals)<\/h3>\n
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    Uniform entropy and energy bounds for fully non-linear equations<\/em>, with D. Phong,<\/div>\n
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    Two Kazdan-Warner-type identities for the renormalized volume coefficients and the Gauss-Bonnet curvatures of a Riemannian metric,<\/i> with Z. Han and H. Li,<\/div>\n
    Pacific J. Math.\u00a0<\/strong>251 (2011), no. 2, 257-268. journal<\/a>; arXiv:0911.4649<\/a><\/div>\n<\/li>\n<\/ol>\n

    Preprints<\/h3>\n
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      On the modulus of continuity of solutions to complex Monge-Amp\u00e8re equations<\/em>, with D.H. Phong, F. Tong and C. Wang,<\/div>\n
      preprint,<\/strong> (2021), arXiv:2112.02354<\/a><\/div>\n<\/li>\n<\/ol>\n

      Thesis and Notes<\/h3>\n
        \n
      1. Geometric invariants and the Monge-Amp\u00e8re equation in K\u00e4hler geometry<\/em>, with D.H. Phong, arXiv:2512.09068<\/a>.<\/li>\n
      2. Auxiliary Complex Monge-Amp\u00e8re Equations in Nonlinear PDE Estimates: A Survey<\/em><\/a>, a survey article written for ICBS, 2024.<\/li>\n
      3. Lecture notes (I<\/a>, II<\/a>, III<\/a>) in a summer school at Tsinghua University, July 2023<\/li>\n
      4. Diameter estimates in K\u00e4hler geometry<\/em><\/a>, Oberwolfach report, Differentialgeometrie im Grossen, July 2 – 7, 2023<\/li>\n
      5. Some parabolic and elliptic problems in complex Riemannian geometry<\/em><\/a>, PhD Thesis, Rutgers University – New Brunswick, 2015<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

        I do research in Geometric Analysis and Complex Differential Geometry. Recently, I am mainly interested in the regularity theory of nonlinear partial differential equations on complex manifolds, and their applications … Read More<\/a><\/p>\n","protected":false},"author":814,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-custom.php","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-5","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"\nResearch - Bin Guo<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/sites.rutgers.edu\/bin-guo\/research\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Research - Bin Guo\" \/>\n<meta property=\"og:description\" content=\"I do research in Geometric Analysis and Complex Differential Geometry. 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