Publications
The partial Legendre transform in Monge-AmpΓ¨re equationsβ (with L. Wang) π Preprint (2024) πPDF
C1,Ξ± regularity of variational problems with a convexity constraintβ (with L. Wang) βπ Preprint (2024) πPDF |πarXiv
βSobolev inequalities and regularity of the linearized complex Monge-AmpΓ¨re and Hessian equationsββ (with J. X. Wang) π Transactions of the American Mathematical Society, 378(2025), 447-475πdoi πarXivβπPDF Liouville theorems for a class of degenerate or singular Monge-AmpΓ¨re equationsβ (with L. Wang) βπβ Journal of Geometric Analysis, 34 (2024), no. 11, Paper No. 352 πdoi πPDF πarXiv Singular Abreu equations and linearized Monge-AmpΓ¨re equations with driftsββ (with Y. H. Kim, N. Q. Le, L. Wang) πβ To appear in Journal of the European Mathematical Society(JEMS) πdoi πPDF πarXiv βTrace inequalities, isocapacitary inequalities and regularity of the complex Hessian equations (with J. X. Wang) π Science China Mathematics 67 (2024), 557-576 πdoi πPDF πarXivβ Interior estimates for Monge-AmpΓ¨re type fourth order equationsβ (with L. Wang) βπβ Revista Matematica Iberoamericana, 39 (2023), no. 5, 1895β1923 πdoi πPDF πarXiv Solvability of a class of singular fourth order equations of Monge-AmpΓ¨re typeββ (with N. Q. Le) πβ Annals of PDE 7 (2021), no. 2, Paper No. 13 πdoi πPDF πarXiv Greenβs function for equations with conic metricsββ (with L. D. Huang) πβ Calculus of Variations and PDE (2021) 60:232 πdoi πPDF Regularity for a class of singular complex Hessian equationsββ (with J. X. Wang) π Acta Mathematica Sinica (Engl. Ser.) 37 (2021), no. 11, 1709-1720 πdoi πPDF πarXiv Monotonicity formulae for the complex Hessian equations (with J. X. Wang) π Methods and Applications of Analysis 28 (2021), No. 1, 77-84 πdoi π PDF πarXiv A priori estimates for the complex Monge-AmpΓ¨re equation (with J. X. Wang, X.-J. Wang)β πβ Peking Mathematical Journal (2021) 4:143-157 πdoi πPDF πarXiv On the four vertex theorem for curves on locally convex surfaces (with S. B. Chen, X.-J. Wang) π Mathematical Research Letters 27(2020), no. 5, 1261-1279 πdoi πPDF πarXiv Moser-Trudinger inequality for the complex Monge-AmpΓ¨re equation (with J. X. Wang, X.-J. Wang) π Journal of Functional Analysis 279 (2020) 108765 πdoi πPDF πarXiv Mabuchi metrics and properness of modified Ding functional (with Y. Li) π Pacific Journal of Mathematics 302(2019), 659-692 πdoi πPDF πarXiv Optimal regularity of plurisubharmonic envelopes on compact Hermitian manifolds (with J. C. Chu) π Science China Mathematics 62 (2019), 371-380 πdoi πPDF πarXiv Relative Algebro-Geometric stabilities of Toric manifoldsββ (with N. Yotsutani) πβ Tohoku Mathematical Journal (2) 71 (2019), no. 4, 495-524 πdoi πPDF πarXiv K-energy on polarized group compactifications of Lie groupsββ (with Y. Li,X. H. Zhu) πβ Journal Functional Analysis 275 (2018), no. 5, 1023-1072 πdoi πPDF πarXiv Variational solutions to extremal metrics on toric surfacesββ πβ Mathematische Zeitschrift 283(2016), 1011-1031 πdoi πPDF πarXiv Modified Futaki invariant and equivariant Riemann-Roch formulaββ (with F. Wang, X. H. Zhu) πβ Advances in Mathematics 289(2016), 1205-1235 πdoi πPDF πarXiv The signed mean curvature measure (with Q. Y. Dai, X.-J. Wang) π Contemporary Mathematics Volume 644(2015) πdoi πPDF πarXiv K-stabilty and canonical metrics on toric manifolds (with X.-J. Wang) π Bulletin of the Institute of Mathematics Academia Sinica(New Series) 9(2014), 85-110 πdoi πPDF πarXiv An obstacle problem for Monge-AmpΓ¨re typed functionals (with J. K. Liu) πβ Journal of Differential Equations 254(2013), 1306-1325 πdoi πPDF πarXiv Sobolev inequality for complex Hessian equations πβ Mathematische Zeitschrift 274(2013), 1306-1325 πdoi πPDF πarXiv Variational problems of Monge-AmpΓ¨re type (with X.-J. Wang) π Fifth International Congress of Chinese Mathematicians Part 1, AMS/IP Studies in Advanced Mathematics Vol. 51, Amer. math. Soc., Providence, RI, 2012, 383-296
The first boundary value problem for Abreuβs equation πInternational Mathematics Research Notice 7(2012), 1439-1484 πdoi πPDF πarXiv The Bernstein theorem for a class of fourth order equations πCalculus of Variations and PDE 43(2012), 25-44 πdoi πPDF πarXiv On the existence and nonexistence of extremal metrics on toric K"ahler surfaces (with X.-J. Wang) π Advances in Mathematics 226(2011), 4429-4455 πdoi πPDF πarXiv Minimizing weak solutions for Calabiβs extremal metrics on toric manifolds (with X. H. Zhu) πCalculus of Variations and PDE 32(2008), 191-217 πdoi πPDF πarXiv K-stability on toric manifolds (with X. H. Zhu) πProceedings of American Mathematical Society 136(2008), 3301-3307 πdoi πPDF πarXiv Relative K-stability and modified K-energy on toric manifolds (with X. H. Zhu) πAdvances in Mathematics 219(2008), 1327-1362 πdoi πPDF πarXiv