Areas of expertise
- Partial Differential Equations 010110
- Calculus Of Variations, Systems Theory And Control Theory 010203
- Algebraic And Differential Geometry 010102
Publications
- Jian, H, Lu, J & Wang, X 2021, 'A boundary expansion of solutions to nonlinear singular elliptic equations', Science China Mathematics.
- Wang, J, Wang, X & Zhou, B 2020, 'Moser-Trudinger inequality for the complex Monge-Ampere equation', Journal of Functional Analysis, vol. 279, no. 12, pp. 1-20.
- Chen, S, Wang, X & Zhou, B 2020, 'On the four vertex theorem for curves on locally convex surfaces', Mathematical Research Letters, vol. 27, no. 5, pp. 1261-1279.
- Wang, X & Wu, Y 2020, 'A new proof for the regularity of Monge-Ampere type equations', Journal of Differential Geometry, vol. 116, no. 3, pp. 543-553.
- Li, Q, Wan, D & Wang, X 2020, 'The Christoffel problem by the fundamental solution of the Laplace equation', Science China Mathematics, vol. 64, pp. 1599-1612.
- Li, Q, Sheng, W & Wang, X 2020, 'Flow by Gauss curvature to the Aleksandrov and dual Minkowski problems', European Mathematical Society Journal, vol. 22, no. 3, pp. 893-923.
- Li, Q, Sheng, W & Wang, X 2019, 'Asymptotic Convergence for a Class of Fully Nonlinear Curvature Flows', Journal of Geometric Analysis, vol. 30, pp. 834-860.
- Chen, S, Liu, J & Wang, X 2019, 'Global regularity of optimal mappings in non-convex domains', Science China Mathematics, vol. 62, no. 11, pp. 2057-2072.
- Li, Q, Santambrogio, F & Wang, X 2019, 'Continuity for the Monge Mass Transfer Problem in Two Dimensions', Archive for Rational Mechanics and Analysis, vol. 231, pp. 1045-1071.
- Chen, H, Huang, G & Wang, X 2019, 'Convergence Rate Estimates for Aleksandrov's Solution to the Monge--Ampère Equation', SIAM Journal of Numerical Analysis, vol. 57, no. 1, pp. 173-191.
- Jian, H, Wang, X & Zhao, Y 2017, 'Global smoothness for a singular Monge-Amp?re equation', Journal of Differential Equations, vol. 263, no. 11, pp. 7250-7262.
- Jian, H, Lu, J & Wang, X 2017, 'A priori estimates and existence of solutions to the prescribed centroaffine curvature problem', Journal of Functional Analysis, vol. [In Press], pp. -.
- Dai, Q, Wang, X & Zhou, B 2016, 'A potential theory for the k-curvature equation', Advances in Mathematics, vol. 288, pp. 791-824.
- Chen, S & Wang, X 2016, 'Strict convexity and C-1,C-alpha regularity of potential functions in optimal transportation under condition A3w', Journal of Differential Equations, vol. 260, no. 2, pp. 1954-1974.
- Santambrogio, F & Wang, X 2016, 'Convexity of the support of the displacement interpolation: Counterexamples', Applied Mathematics Letters, vol. 58, pp. 152-158.
- He, Y, Li, Q & Wang, X 2016, 'Multiple solutions of the L-p-Minkowski problem', Calculus of Variations and Partial Differential Equations, vol. 55, no. 5, pp. 117 (1-13pp).
- Dai, Q, Wang, X & Zhou, B 2015, 'The signed mean curvature measure', Complex Mathematic: Analysis, Complex Geometry, and Mathematical Physics: In Honor of Duong H. Phong, ed. P M N Feehan, J Song, B Weinkove & R A Wentworth, American Mathematical Society, USA, pp. 23-32pp.
- Jin, Y, Li, D & Wang, X 2015, 'Regularity and analyticity of solutions in a direction for elliptic equations', Pacific Journal of Mathematics, vol. 276, no. 2, pp. 419-436.
- Li, Q & Wang, X 2015, 'Regularity of the homogeneous Monge-Ampere equation', Discrete and Continuous Dynamical Systems, Series A, vol. 35, no. 12, pp. 6069-6084pp.
- Liu, J, Trudinger, N & Wang, X 2015, 'On Asymptotic Behaviour and W-2,W-p Regularity of Potentials in Optimal Transportation', Archive for Rational Mechanics and Analysis, vol. 215, no. 3, pp. 867-905.
- Liu, J & Wang, X 2015, 'Interior a priori estimates for the Monge-Ampère equation', in Huai-Dong Cao, Richard Schoen, Shing-Tung Yau (ed.), Surveys in Differential Geometry Volume 19 (2014), International Press, Somerville, MA, U.S.A., pp. 151 - 177pp.
- Jian, H, Lu, J & Wang, X 2015, 'Nonuniqueness of solutions to the Lp-Minkowski problem', Advances in Mathematics, vol. 281, pp. 845-856.
- Li, Q, Santambrogio, F & Wang, X 2014, 'Regularity in Monge's mass transfer problem', Journal de Mathematiques Pures et Appliquees, vol. 102, no. 6, pp. 1015-1040.
- Wang, X 2014, 'Counterexample to the convexity of level sets of solutions to the mean curvature equation', European Mathematical Society Journal, vol. 16, no. 6, pp. 1173-1182.
- Jian, H & Wang, X 2014, 'EXISTENCE OF ENTIRE SOLUTIONS TO THE MONGE-AMPERE EQUATION', American Journal of Mathematics, vol. 136, no. 4, pp. 1093-1106.
- Wang, X & Zhou, B 2014, 'K-STABILITY AND CANONICAL METRICS ON TORIC MANIFOLDS', Bulletin of the Institute of Mathematics, Academia Sinica (New Series), vol. 9, no. 1, pp. 85-110.
- Jian, H & Wang, X 2014, 'Optimal boundary regularity for nonlinear singular elliptic equations', Advances in Mathematics, vol. 251, no. 30 January 2014, pp. 111-126.
- Jian, H & Wang, X 2013, 'Bernstein theorem and regularity for a class of monge-ampére equations', Journal of Differential Geometry, vol. 93, no. 3, pp. 431-469.
- Lu, J & Wang, X 2013, 'Rotationally symmetric solutions to the Lp- Minkowski problem', Electronic Journal of Differential Equations, vol. 254, no. 3, pp. 983-1005.
- Tian, G & Wang, X 2013, 'A priori estimates for fully nonlinear parabolic equations', International Mathematics Research Notices, vol. 2012, no. 17, pp. 3857-3877.
- Sheng, W, Trudinger, N & Wang, X 2012, 'The k-Yamabe problem', in Huai-Dong Cao; Shing-Tung Yau (ed.), Surveys in Differential Geometry Volume 17, International Press, USA, pp. 427-457.
- Sheng, W, Trudinger, N & Wang, X 2012, 'Prescribed Weingarten Curvature Equations', in Yuxin Dong; Jixiang Fu; Guozhen Lu; Weimin Sheng; Xiaohua Zhu (ed.), Recent Developments in Geometry and Analysis, International Press, USA, pp. 359-386.
- Tian, G & Wang, X 2012, 'A perturbation method for elliptic and parabolic equations', in Yibing Shen; Zhongmin Shen; Shing-Tung Yau (ed.), Differential Geometry: Under the Influence of S.-S. Chern, Higher education press and international press, USA, pp. 81-100.
- Wang, X & Zhou, B 2012, 'Variational problems of Monge-Ampère type', in Lizhen Ji (ed.), AMS/IP Studies in Advanced Mathematics, Fifth International Congress of Chinese Mathematicians Part 1, International Press, United States of America, pp. 383-396pp.
- Dai, Q, Trudinger, N & Wang, X-J 2012, 'The mean curvature measure', Journal of European Mathematical Society, vol. 14, no. 3, pp. 779-800.
- Wang, X-J & Zhou, B 2011, 'On the existence and nonexistence of extremal metrics on toric Kähler surfaces', Advances in Mathematics, vol. 226, no. 5, pp. 4429-4455.
- Wang, X-J 2011, 'Convex solutions to the mean curvature flow', Annals of Mathematics, vol. 173, no. 3, pp. 1185-1239.
- Karakhanyan, A & Wang, X-J 2010, 'On the reflector shape design', Journal of Differential Geometry, vol. 84, no. 3, pp. 561-610.
- Liu, J, Trudinger, N & Wang, X-J 2010, 'Interior C 2,alpha regularity for potential functions in optimal transportation', Communications in Partial Differential Equations, vol. 35, no. 1, pp. 165-184.
- Tian, G & Wang, X-J 2010, 'Moser-Trudinger type inequalities for the Hessian equation', Journal of Functional Analysis, vol. 259, no. 8, pp. 1974-2002.
- Tian, G & Wang, X-J 2010, 'Partial regularity for elliptic equations', Discrete and Continuous Dynamical Systems, Series A, vol. 28, no. 3, pp. 899-913.
- Gursky, M, Lanconelli, E, Malchiodi, A et al 2009, 'The k-hessian equation', Lecture Notes in Mathematics, vol. 1977, pp. 177-252.
- Trudinger, N & Wang, X-J 2010, 'The intermediate case of the Yamabe problem for higher order curvatures', International Mathematics Research Notices, vol. 227, pp. 1-22.
- Sheng, W & Wang, X-J 2009, 'Singularity profile in the mean curvature flow', Methods and Applications of Analysis, vol. 16, no. 2, pp. 139 - 155.
- Trudinger, N & Wang, X-J 2009, 'On Harnack inequalities and singularities of admissible metrics in the Yamabe problem', Calculus of Variations and Partial Differential Equations, vol. 35, no. 3, pp. 317-338.
- Trudinger, N & Wang, X-J 2009, 'On strict convexity and continuous differentiability of potential functions in optimal transportation', Archive for Rational Mechanics and Analysis, vol. 192, no. 3, pp. 403-418.
- Trudinger, N & Wang, X-J 2009, 'On the second boundary value problem for Monge-Ampere type equations and optimal transportation', Annali Della Scuola Normale Superiore di Pisa, vol. 8, no. 1, pp. 143-174.
- Trudinger, N & Wang, X-J 2009, 'Quasilinear Elliptic Equations with Signed Measure Data', Discrete and Continuous Dynamical Systems, Series A, vol. 23, no. 1 & 2, pp. 477-494.
- Wang, X-J 2009, 'The k-Hessian equation', in Alice Chang, Andrea Malchiodi and Antonio Ambrosetti (ed.), Geometric Analysis and PDEs, Springer, Dordrecht, pp. 177-252.
- Trudinger, N & Wang, X-J 2008, 'Boundary regularity for the Monge-Ampere and affine maximal surface equations', Annals of Mathematics, vol. 167, no. 3, pp. 993-1028.
- Trudinger, N & Wang, X-J 2008, 'The Monge-Ampere equation and its geometric applications', in Lizhen Ji; Peter Li; Richard Schoen; Leon Simon (ed.), Handbook of Geometric Analysis (Volume 1), Higher Education Press, Somerville, USA, pp. 467-524.
- Wang, X-J & Tian, G 2008, 'A class of Sobolev type inequalities', Methods and Applications of Analysis, vol. 15, no. 2, pp. 263-276.
- Jian, H & Wang, X-J 2007, 'Continuity estimates for the Monge-Ampere equation', SIAM Journal on Mathematical Analysis, vol. 39, no. 2, pp. 608-626.
- Karakhanyan, A & Wang, X-J 2007, 'The reflector design problem', International Congress of Chinese Mathematicians (ICCM 2007), Higher Education Press, China, pp. 89-109.
- Sheng, W, Trudinger, N & Wang, X-J 2007, 'The Yamabe problem for higher order curvatures', Journal of Differential Geometry, vol. 77, pp. 515-553.
- Chou, K & Wang, X-J 2006, 'The Lp-Minkowski problem and the Minkowski problem in centroaffine geometry', Advances in Mathematics, vol. 205, pp. 33-83.
- Sheng, W, Trudinger, N & Wang, X-J 2006, 'Enclosed convex hypersurfaces with maximal affine area', Mathematische Zeitschrift, vol. 252, pp. 497-510.
- Wang, X-J 2006, 'A priori estimates and existence for a class of fully nonlinear elliptic equations in conformal geometry', Chinese Annals of Mathematics Series B, vol. 27, pp. 169-178.
- Wang, X-J 2006, 'Schauder estimates for elliptic and parabolic equations', Chinese Annals of Mathematics Series B, vol. 27B, no. 6, pp. 637-642.
- Trudinger, N & Wang, X-J 2005, 'The affine Plateau problem', Journal of the American Mathematical Society, vol. 18, no. 2, pp. 253-289.
- Trudinger, N, Ma, X & Wang, X-J 2005, 'Regularity of Potential Functions of the Optimal Transportation Problem', Archive for Rational Mechanics and Analysis, vol. 177, pp. 151-183.
- Wang, X-J 2005, 'A note on the Yamabe problem', Journal of Partial Differential Equations, vol. 18, no. 4, pp. 322-326.
- Ivochkina, N, Trudinger, N & Wang, X-J 2004, 'The Dirichlet Problem for degenerate Hessian Equations', Communications in Partial Differential Equations, vol. 29, pp. 219-235.
- Ivochkina, N, Trudinger, N & Wang, X-J 2005, 'The Dirichlet Problem for Degenerate Hessian Equations', Communications in Partial Differential Equations, vol. 29, no. 1&2, pp. 219-235.
- Sheng, W, Trudinger, N & Wang, X-J 2004, 'Convex hypersurfaces of prescribed Weingarten curvatures', Communications in Analysis and Geometry, vol. 12, no. 1, pp. 213-232.
- Sheng, W, Urbas, J & Wang, X-J 2004, 'Interior curvature bounds for a class of curvature equations', Duke Mathematical Journal, vol. 123, no. 2, pp. 235-264.
- Wang, X-J & Zhu, X 2004, 'Kahler-Ricci solitons on toric manifolds with positive first Chern class', Advances in Mathematics, vol. 188, pp. 87-103.
- Wang, X-J 2004, 'On the design of a reflector antenna 2', Calculus of Variations and Partial Differential Equations, vol. 20, pp. 329-341.
- Wang, X-J 2004, 'The Monge Optimal transportation problem', International Congress of Chinese Mathematicians (ICCM 2001), ed. CS Lin, Lo Yang and ST Yau, International Press, USA, pp. 537-545.
- Trudinger, N & Wang, X-J 2002, 'Affine complete locally convex hypersurfaces', Inventiones Mathematicae, vol. 150, pp. 45-60.
- Trudinger, N & Wang, X-J 2002, 'Bernstein-Jorgens Theorem for a Fourth Order Partial Differential Equation', Journal of Partial Differential Equations, vol. 15, no. 1, pp. 78-88.
- Trudinger, N & Wang, X-J 2002, 'Hessian Measures III', Journal of Functional Analysis, vol. 193, pp. 1-23.
- Trudinger, N & Wang, X-J 2002, 'On locally convex hypersurfaces with boundary', Journal fur Reine und Angewandte Mathematik, vol. 551, pp. 11-32.
- Trudinger, N & Wang, X-J 2002, 'On the weak continuity of Elliptic Operators and applications to Potential Theory', American Journal of Mathematics, vol. 124, no. 2, pp. 369-410.
- Wang, X-J 2002, 'Affine maximal hypersurfaces', in Tatsien, LI (ed.), Proceedings of the International Congress of Mathematicians, Higher Education Press, Beijing, China, pp. 221-231.
- Chou, K & Wang, X-J 2001, 'A variational theory of the Hessian equation', Communications on Pure and Applied Mathematics, vol. 54, pp. 1029-1064.
- Trudinger, N & Wang, X-J 2001, 'On the Monge mass transfer problem', Calculus of Variations and Partial Differential Equations, vol. 13, pp. 19-31.
- Trudinger, N & Wang, X-J 2000, 'The Bernstein problem for affine maximal hypersurfaces', Inventiones Mathematicae, vol. 140, no. 2, pp. 399 - 422.
- Guan, P., Trudinger, N, & Wang, X.-J 1999, 'On the Dirichlet problem for degenerate Monge-Amp\`ere equations', Acta Mathematica, vol. 182, no. 1, pp. 87-104.
- Trudinger, N & Wang, X-J 1999, 'Hessian Measures II', Annals of Mathematics, vol. 150, no. 2, pp. 579-604.
