| Introduction | Publications |
Visiting | Chinese Version |
My publications:
61. Daowen Lin, Xi-Nan Ma, Best constant and extremal functions for a class Hardy-Sobolev-Maz'ya inequalities., arXiv preprint arXiv:2412.09033.
60. Xi-Nan Ma, Wangzhe Wu, The weak convergence for a measure related to a class of conformally invariant fully nonlinear operator, arXiv preprint arXiv:2407.17736.
59. Xi-Nan Ma, Qianzhong Ou, Tian Wu, Jerison-Lee identity and Semi-linear subelliptic equation on CR manifold, arXiv preprint arXiv:2311.16428.
58. Xi-Nan Ma, Wangzhe Wu, Liouville theorem for elliptic equations with a source reaction term involving the product of the function and its gradient in \(\mathbb R^n\), arXiv preprint arXiv:2311.04652.
57. Xi-Nan Ma, Wangzhe Wu, Qiqi Zhang, Liouville theorem for elliptic equations involving the sum of the function and its gradient in \(\mathbb R^n\), arXiv preprint arXiv:2311.04641.
56. Zhenghuan Gao, Xi-Nan Ma, Dekai Zhang, The Dirichlet problem of homogeneous complex \(k\)-Hessian equation in a \((k-1)\)-pesudoconvex domain with isolated singularity, arXiv preprint arXiv:2304.08407.
55. Zhenghuan Gao, Xi-Nan Ma, Dekai Zhang, The Dirichlet problem of the homogeneous \(k\)-Hessian equation in a punctured domain, arXiv preprint arXiv:2303.07976.
54. Xi-Nan Ma, Dekai Zhang, The exterior Dirichlet problem for the homogeneous \(k\)-Hessian equation, arXiv preprint arXiv: 2207.13504.
53. Yong Liu, Xi-Nan Ma, Juncheng Wei, Wangzhe Wu, Entire solutions of the magnetic Ginzburg-Landau equation in \(\mathbb R^4\), Ann. Scuola Norm. Sup. Pisa Cl. Sci. accepted.
52. Xi-Nan Ma, Qianzhong Ou, Tian Wu, Jerison-Lee identities and semi-linear subelliptic equations on Heisenberg group, Acta Math. Sci. Ser. B (Engl. Ed.) 45 (2025), no. 1, 264–279.
51. Xi-Nan Ma, Tian Wu, The application of the invariant tensor technique in the classification of solutions to semilinear elliptic and sub-elliptic partial differential equations, SCIENTIA SINICA Mathematica , Volume 54, Issue 10: 1627 (2024).
50. Daowen Lin, Xi-Nan Ma, Liouville type theorem for a class quasilinear p-Laplace type equation on the sphere, Math. Ann. 389 (2024), no. 3, 2273–2287.
49. Xiaohan Jia, Xi-Nan Ma, Shujun Shi, Convexity estimates for Green's function and the first eigenfunction of Laplace operator, Potential Anal. 59 (2023), no. 4, 1525–1545.
48. Bin Deng, Xi-Nan Ma, Gradient estimates for the solutions of higher order curvature equations with prescribed contact angle, Math. Eng. 5 (2023), no. 6, Paper No. 093, 13 pp.
47. Xiaohan Jia, Xi-Nan Ma, Shujun Shi, Remarks on convexity estimates for solutions of the torsion problem, Sci. China Math. 66 (2023), no. 5, 1003–1020.
46. Zhenghuan Gao, Xi-Nan Ma, Dekai Zhang, The exterior Dirichlet problem for the homogeneous complex \(k\)-Hessian equation, Adv. Nonlinear Stud. 23 (2023), no. 1, Paper No. 20220039, 33 pp.
45. Xi-Nan Ma, Qianzhong Ou, A Liouville theorem for a class semilinear elliptic equations on the Heisenberg group, Adv. Math. 413 (2023), Paper No. 108851, 20 pp.
44. Daowen Lin, Xi-Nan Ma, Qianzhong Ou, The Obata type integral identity and its allpications., Surveys in Geometric Anaysis 2021.
43. Chuanqiang Chen, Xi-Nan Ma, Dekai Zhang, The Neumann problem for parabolic Hessian quotient equations, Acta Math. Sin. (Engl. Ser.) 37 (2021), no. 9, 1313–1348.
42. Xi-Nan Ma, Wei Zhang, Superharmonicity of curvature function for the convex level sets of harmonic functions, Calc. Var. Partial Differential Equations 60 (2021), no. 4, Paper No. 141, 12 pp.
41. Zhenghuan Gao, Xi-Nan Ma, Peihe Wang, Liangjun Weng, Nonparametric mean curvature flow with nearly vertical contact angle condition, J. Math. Study 54 (2021), no. 1, 28–55.
40. Chuanqiang Chen, Xi-Nan Ma, Wei Wei, The Neumann problem of special Lagrangian equations with supercritical phase, J. Differential Equations 267 (2019), no. 9, 5388–5409.
39. Chuanqiang Chen, Xi-Nan Ma, P. Salani, On space-time quasiconcave solutions of the heat equation, Mem. Amer. Math. Soc. 259 (2019), no. 1244, v+81 pp.
38. Chuanqiang Chen, Xi-Nan Ma, Wei Wei, The Neumann problem of complex special Lagrangian equations with supercritical phase, Anal. Theory Appl. 35 (2019), no. 2, 144–162.
37. Xi-Nan Ma, Guohuan Qiu, The Neumann problem for Hessian equations, Comm. Math. Phys. 366 (2019), no. 1, 1–28.
36. Chuanqiang Chen, Xi-Nan Ma, The microscopic convexity of level sets of solutions for elliptic and parabolic equations, Scientia SINICA Mathematica (2018), no. 10, 1205-1218. (in Chinese)
35. Xi-Nan Ma, Peihe Wang, Boundary gradient estimate of the solution to mean curvature equations with Neumann boundary or prescribed contact angle boundary, Scientia SINICA Mathematica (2018), no. 1, 213-226. (in Chinese)
34. Xi-Nan Ma, Peihe Wang, Wei Wei, Constant mean curvature surfaces and mean curvature flow with non-zero Neumann boundary conditions on strictly convex domains, J. Funct. Anal. 274 (2018), no. 1, 252–277.
33. Xi-Nan Ma, Convexity of the solutions of elliptic and parabolic equations, University mathematicas, Vol. 32 (2016), no. 5, 1-17. (in Chinese)
32. Xi-Nan Ma, Jinju Xu, Gradient estimates of mean curvature equations with Neumann boundary value problems, Adv. Math. 290 (2016), 1010–1039.
31. Chuanqiang Chen, Xi-Nan Ma, Shujun Shi, Curvature estimates for the level sets of solutions to the Monge-Ampère equation \(\det\mathrm{D}^2u=1\), Chinese Ann. Math. Ser. B 35 (2014), no. 6, 895–906.
30. Xi-Nan Ma, Yongbing Zhang, The convexity and the Gaussian curvature estimates for the level sets of harmonic functions on convex rings in space forms, J. Geom. Anal. 24 (2014), no. 1, 337–374.
29. Xi-Nan Ma, Wei Zhang, The concavity of the Gaussian curvature of the convex level sets of \(p\)-harmonic functions with respect to the height, Commun. Math. Stat. 1 (2013), no. 4, 465–489.
28. Xi-Nan Ma, Shujun Shi, Yu Ye, The convexity estimates for the solutions of two elliptic equations, Comm. Partial Differential Equations 37 (2012), no. 12, 2116–2137.
27. J. Jost, Xi-Nan Ma, Qianzhong Ou, Curvature estimates in dimensions 2 and 3 for the level sets of \(p\)-harmonic functions in convex rings, Trans. Amer. Math. Soc. 364 (2012), no. 9, 4605–4627.
26. Bowen Hu, Xi-Nan Ma, A constant rank theorem for spacetime convex solutions of heat equation, Manuscripta Math. 138 (2012), no. 1-2, 89–118.
25. Baojun Bian, Pengfei Guan, Xi-Nan Ma, Lu Xu, A constant rank theorem for quasiconcave solutions of fully nonlinear partial differential equations, Indiana Univ. Math. J. 60 (2011), no. 1, 101–119.
24. Fei Han, Xi-Nan Ma, Damin Wu, The existence of \(k\)-convex hypersurface with prescribed mean curvature, Calc. Var. Partial Differential Equations 42 (2011), no. 1-2, 43–72.
23. Hao Fang, Mijia Lai, Xi-Nan Ma, On a class of fully nonlinear flows in Kähler geometry, J. Reine Angew. Math. 653 (2011), 189–220.
22. Xi-Nan Ma, Jiang Ye, Yunhua Ye, Principal curvature estimates for the level sets of harmonic functions and minimal graphs in \(\mathbb{R}^3\), Commun. Pure Appl. Anal. 10 (2011), no. 1, 225–243.
21. Pengfei Guan, Xi-Nan Ma, N. Trudinger, Xiaohua Zhu, A form of Alexandrov-Fenchel inequality, Pure Appl. Math. Q. 6 (2010), no. 4, Special Issue: In honor of Joseph J. Kohn. Part 2, 999–1012.
20. Pan Liu, Xi-Nan Ma, Lu Xu, A Brunn-Minkowski inequality for the Hessian eigenvalue in three-dimensional convex domain, Adv. Math. 225 (2010), no. 3, 1616–1633.
19. Xi-Nan Ma, Qianzhong Ou, Wei Zhang, Gaussian curvature estimates for the convex level sets of \(p\)-harmonic functions, Comm. Pure Appl. Math. 63 (2010), no. 7, 935–971.
18. Zuoliang Hou, Xi-Nan Ma, Damin Wu, A second order estimate for complex Hessian equations on a compact Kähler manifold, Math. Res. Lett. 17 (2010), no. 3, 547–561.
17. Xi-Nan Ma, Qianzhong Ou, The convexity of level sets for solutions to partial differential equations, Adv. Lect. Math. (ALM), 10 (2010), Trends in partial differential equations, 295-322.
16. A. Chang, Xi-Nan Ma, P. Yang, Principal curvature estimates for the convex level sets of semilinear elliptic equations, Discrete Contin. Dyn. Syst. 28 (2010), no. 3, 1151–1164.
15. Changqing Hu, Xi-Nan Ma, Qianzhong Ou, A constant rank theorem for level sets of immersed hypersurfaces in \(\mathbb{R}^{n+1}\) with prescribed mean curvature, Pacific J. Math. 245 (2010), no. 2, 255–271.
14. Fei Han, Xi-Nan Ma, Damin Wu, A constant rank theorem for Hermitian k-convex solutions of complex Laplace equations, Methods Appl. Anal. 16 (2009), no. 2, 263–289.
13. Pengfei Guan, Changshou Lin, Xi-Nan Ma, The existence of convex body with prescribed curvature measures, Int. Math. Res. Not. IMRN 2009, no. 11, 1947–1975.
12. Xi-Nan Ma, Lu Xu, The convexity of solution of a class Hessian equation in bounded convex domain in \(\mathbb{R}^3\), J. Funct. Anal. 255 (2008), no. 7, 1713–1723.
11. L. Caffarelli, Pengfei Guan, Xi-Nan Ma, A constant rank theorem for solutions of fully nonlinear elliptic equations, Comm. Pure Appl. Math. 60 (2007), no. 12, 1769–1791.
10. Pengfei Guan, Changshou Lin, Xi-Nan Ma, The Christoffel-Minkowski problem. II. Weingarten curvature equations, Chinese Ann. Math. Ser. B 27 (2006), no. 6, 595–614.
9. Pengfei Guan, Xi-Nan Ma, Feng Zhou, The Christofel-Minkowski problem. III. Existence and convexity of admissible solutions, Comm. Pure Appl. Math. 59 (2006), no. 9, 1352–1376.
8. Xi-Nan Ma, N. Trudinger, Xu-Jia Wang, Regularity of potential functions of the optimal transportation problem, Arch. Ration. Mech. Anal. 177 (2005), no. 2, 151–183.
7. Pengfei Guan, Xi-Nan Ma, Convex solutions of fully nonlinear elliptic equations in classical differential geometry, Contemp. Math., 367 (2005), 115-127.
6. Changqing Hu, Xi-Nan Ma, Chunli Shen, On the Christoffel-Minkowski problem of Firey's \(p\)-sum., Calc. Var. Partial Differential Equations 21 (2004), no. 2, 137–155.
5. Pengfei Guan, Xi-Nan Ma, The Christoffel-Minkowski problem. I. Convexity of solutions of a Hessian equation., Invent. Math. 151 (2003), no. 3, 553–577.
4. Xi-Nan Ma, Concavity estimates for a class of nonlinear elliptic equations in two dimensions, Math. Z. 240 (2002), no. 1, 1–11.
3. Xi-Nan Ma, Sharp size estimates for capillary free surfaces without gravity, Pacific J. Math. 192 (2000), no. 1, 121–134.
2. Xi-Nan Ma, A sharp minimum principle for the problem of torsional rigidity, J. Math. Anal. Appl. 233 (1999), no. 1, 257–265.
1. Xi-Nan Ma, A necessary condition of solvability for the capillarity boundary of Monge-Ampère equations in two dimensions, Proc. Amer. Math. Soc. 127 (1999), no. 3, 763–769.