Prof. Jingang Xiong (熊金钢)

Contact Information

Address Main Building 1216, School of Mathematical Sciences,
Beijing Normal University, Beijing 100875, China
Email jx@bnu.edu.cn

Curriculum Vitae

中文版 English Version

Preprints & Publications

  1. Sharp global Alexandrov estimates and entire solutions of Monge-Amp\`ere equationss (with T. Jin and X. Tu). Preprint. arXiv
  2. Extremal Alexandrov estimates: singularities, obstacles, and stability (with T. Jin and X. Tu). Preprint. arXiv
  3. On some divergence-form singular elliptic equations with codimension-two boundary: $L^p$-estimates (with J. Ji). Preprint. arXiv
  4. On the singular set of the free boundary for a Monge-Amp\`ere obstacle problem (with T. Jin and X. Tu). Accepted by Communications in Analysis and Geometry. arXiv
  5. The Mass-Angular Momentum Inequality for Multiple Black Holes (with Q. Han, M. Khuri and G. Weinstein). Preprint. arXiv
  6. Extinction profiles for the Sobolev critical fast diffusion equation in bounded domains. I. One bubble dynamics (with T. Jin). Arch. Ration. Mech. Anal. 250 (2026), no. 2, Paper No. 14. arXiv
  7. Asymptotic analysis of harmonic maps with prescribed singularities (with Q. Han, M. Khuri and G. Weinstein). Preprint. arXiv
  8. Regularity and classification of the free boundary for a Monge-Amp\`ere obstacle problem (with T. Jin and X. Tu). Adv. Math 482 (2025), Art. No. 110602. arXiv
  9. Regularity of solutions to the Dirichlet problem for fast diffusion equations (with T. Jin). Adv. Math 478 (2025), Art. No. 110390. arXiv
  10. A survey of the isolated singularity problems for the Yamabe equation (in Chinese, joint with X. Du, T. Jin and H. Yang). SCIENTIA SINICA Mathematica 55 (2025), 1029--1058.
  11. A dual Yamabe flow and related integral flows. Chin. Ann. Math. Ser. B. 45 (2024), 319--348. arXiv
  12. Holder regularity for the linearized porous medium equation in bounded domains (with T. Jin). Anal. Theory Appl. 40 (2024), 111--171. arXiv
  13. Stability of the separable solutions for a nonlinear boundary diffusion problem (with T. Jin and X. Yang). J. Math. Pures Appl. 183 (2024), 1--43. arXiv
  14. Optimal regularity and fine asymptotics for the porous medium equation in bounded domains (with T. Jin and X. Ros-Oton). J. Reine Angew. Math. 809 (2024), 269--300. arXiv
  15. Regularity of viscosity solutions of the $\sigma_k$-Loewner-Nirenberg problem (with Y.Y. Li and L. Nguyen). Proc. London Math. Soc. 127 (2023), no. 4, 1--34. arXiv
  16. Asymptotic behavior of solutions to the Yamabe equation with an asymptotically flat metric (with Z.-C. Han and L. Zhang). J. Funct. Anal. 285 (2023), 109982. arXiv
  17. Bubbling and extinction for some fast diffusion equations in bounded domains (with T. Jin). Trans. Amer. Math. Soc. Ser. B 10 (2023), 1287--1332. arXiv
  18. Blow up limits of the fractional Laplacian and their applications to the fractional Nirenberg problem (with X. Du, T. Jin and H. Yang). Proc. Amer. Math. Soc. 151 (2023), no. 11, 4693--4701. arXiv
  19. Optimal boundary regularity for fast diffusion equations in bounded domains (with T. Jin). Amer. J. Math. 145 (2023), no. 1, 151--220. arXiv
  20. Singular extinction profiles of solutions to some fast diffusion equations (with T. Jin). J. Funct. Anal. 283 (2022), 109595. arXiv
  21. Isolated singularities of solutions to the Yamabe equation in dimension 6 (with L. Zhang). Int. Math. Res. Not. (IMRN) Vol. 2022, No. 12, 9571--9597. arXiv
  22. On a Rayleigh-Faber-Krahn inequality for the regional fractional Laplacian (with T. Jin and D. Kriventsov). Ann. Appl. Math. 37 (2021), 363--393. arXiv
  23. Sharp Sobolev inequalities involving boundary terms revisited (with Z. Tang and N. Zhou).Calc. Var. Partial Differential Equations 60 (2021), no. 6, Paper No. 160, 26 pp. arXiv
  24. Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularities (with T. Jin). Ann. Inst. Henri Poincare, Analyse Nonlineaire 38 (2021), 1167--1216. arXiv
  25. Existence of entire solutions of Monge-Amp\`ere equations with prescribed asymptotic behaviors (with J. Bao, Z. Zhou). Calc. Var. Partial Differential Equations 58 (2019), no. 6, Paper No. 193, 12 pp. arXiv
  26. Compactness of conformal metrics with constant $Q$-curvature. I (with Y.Y. Li). Adv. Math 345 (2019), 116--160. arXiv
  27. On the isoperimetric quotient over scalar-flat conformal classes (with T. Jin). Comm. Partial Differential Equations 43 (2018), no. 12, 1737--1760. arXiv
  28. A derivation of the sharp Moser-Trudinger-Onofri inequalities from the fractional Sobolev inequalities. Peking Math J. 1 (2018), no. 2, 221--229. arXiv
  29. On a conformally invariant integral equation involving Poisson kernel. Acta Mathematica Sinica, English Series 34 (2018), no. 4, 681--690. arXiv
  30. Minimizers for the fractional Sobolev inequality on domains (with R. L. Frank, T. Jin). Calc. Var. Partial Differential Equations 57 (2018), no. 2, Art. 43, 31 pp. arXiv
  31. Compactness of solutions to nonlocal elliptic equations (with M. Niu, Z. Peng). J. Funct. Anal. 275(2018), 2333--2372. arXiv
  32. The critical semilinear elliptic equation with boundary isolated singularities. J. Differential Equations 263 (2017), no. 3, 1907--1930.
  33. On local behavior of singular positive solutions to nonlocal elliptic equations (with T. Jin, O S. de Queiroz, Y. Sire). Calc. Var. Partial Differential Equations 56 (2017), no. 1, Art. 9, 25 pp. arXiv
  34. Classification theorems for solutions of higher order boundary conformally invariant problems, I (with L. Sun). J. Funct. Anal. 271 (2016), 3727--3764. arXiv
  35. The Nirenberg problem and its generalizations: A unified approach (with T. Jin, Y.Y. Li). Math. Ann. 369 (2017), no. 1-2, 109--151. arXiv
  36. Schauder estimates for nonlocal fully nonlinear equations (with T. Jin). Ann. Inst. Henri Poincare, Analyse Nonlineaire. 33 (2016), 1375--1407. arXiv
  37. Schauder estimates for solutions of linear parabolic integro-differential equations (with T. Jin). Discrete Contin. Dyn. Syst. 35 (2015), no 12, 5977--5998.
  38. Solutions of some Monge-Amp\`ere equations with isolated and line singularities (with T. Jin). Adv. Math 289 (2016), 114--141.
  39. Boundary Gradient Estimates for Parabolic and Elliptic Systems from Linear Laminates (with H. Dong). Int. Math. Res. Not. (IMRN) 2015 (2015), 7734--7756.
  40. A sharp Sobolev trace inequality involving the mean curvature on Riemannian manifolds (with T. Jin). Trans. Amer. Math. Soc. 367 (2015), 6751--6770.
  41. On a fractional Nirenberg problem, part II: existence of solutions (with T. Jin, Y.Y. Li). Int. Math. Res. Not. (IMRN) 2015 (2015), no. 6, 1555--1589.
  42. Existence and asymptotics for solutions of a non-local $Q$-curvature equation in dimension three (with T. Jin, A. Maalaoui, L. Martinazzi). Calc. Var. Partial Differential Equations 52 (2015), no. 3-4, 469--488.
  43. A fractional Yamabe flow and some applications (with T. Jin). J. Reine Angew. Math. 696 (2014), 187--223.
  44. On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions (with T. Jin, Y.Y. Li). J. Eur. Math. Soc. (JEMS) 16 (2014), no. 6, 1111--1171.
  45. Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities (with L. Caffarelli, T. Jin, Y. Sire). Arch. Ration. Mech. Anal. 213 (2014), no. 1, 245--268.
  46. A Liouville theorem for solutions of degenerate Monge-Amp\`ere equations (with T. Jin). Comm. Partial Differential Equations 39 (2014), no. 2, 306--320.
  47. Sharp constants in weighted trace inequalities on Riemannian manifolds (with T. Jin). Calc. Var. Partial Differential Equations 48 (2013), no. 3-4, 555--585.
  48. Sharp regularity for elliptic systems associated with transmission problems (with J. Bao). Potential Anal. 39 (2013), no. 2, 169--194.
  49. $C^{1,1}$ estimates for elliptic equations with partial and piecewise continuous coefficients. Methods Appl. Anal. 18 (2011), no. 4, 373--389.
  50. A Harnack inequality for fractional Laplace equations with lower order terms (with J. Tan). Discrete Contin. Dyn. Syst. 31 (2011), no. 3, 975--983.
  51. The obstacle problem for Monge-Amp\`ere type equations in non-convex domains (with J. Bao). Commun. Pure Appl. Anal. 10 (2011), no. 1, 59--68.
  52. On J\"orgens, Calabi, and Pogorelov type theorem and isolated singularities of parabolic Monge-Amp\`ere equations (with J. Bao). J. Differential Equations 250 (2011), no. 1, 367--385.