Publications

1. Singularity theorems and the Lorentzian splitting theorem for the Bakry-Emery-Ricci tensor, J. Geom. Phys. 60(3):477–490, 2010.
   Journal link.  arXiv preprint.

2. On the nonexistence of quasi-Einstein metrics, Pacific J. Math. 248(2):277–284, 2010.
   Journal link.  arXiv preprint.

3. (with Yujen Shu and Guofang Wei) Rigidity of quasi-Einstein metrics, Diff. Geo. Appl., 29(1):93–100, 2011.
   Journal link.  arXiv preprint.

4. Smooth metric measure spaces, quasi-Einstein metrics, and tractors, Cent. Eur. J. Math., 10(5):1733–1762, 2012.
   Journal link.  arXiv preprint.

5. Smooth metric measure spaces and quasi-Einstein metrics, Internat. J. Math., 23(10):1250110, 36 pp., 2012.
   Journal link.  arXiv preprint.

6. Sharp metric obstructions for quasi-Einstein metrics, J. Geom. Phys., 64(2):12–30, 2013.
   Journal link.  arXiv preprint.

7. Conformal invariants measuring the best constants for Gagliardo-Nirenberg-Sobolev inequalities, Calc. Var. PDE, 48(3-4):507–526, 2013.
   Journal link.  arXiv preprint.

8. (with Paul Yang) A Paneitz-type operator for CR pluriharmonic functions, Bull. Inst. Math. Acad. Sin. (N.S.), 8(3):285–322, 2013.
   Journal link.  arXiv preprint.

9. The energy of a smooth metric measure space and applications, J. Geom. Anal., 25(1):616–667, 2015.
   Journal link.  arXiv preprint.

10. (with Sagun Chanillo and Paul Yang) A remark on the kernel of the CR Paneitz operator, Nonlinear Analysis, 126:153–158, 2015.
    Journal link.  arXiv preprint.

11. A Yamabe-type problem on smooth metric measure spaces, J. Differential Geom., 101(3):467–505, 2015.
    Journal link.  arXiv preprint.

12. (with Sagun Chanillo and Paul Yang) The CR Paneitz operator and the stability of CR pluriharmonic functions, Adv. Math., 287:109–122, 2016.
    Journal link.  arXiv preprint.

13. (with Chin-Yu Hsiao and Paul Yang) Extremal metrics for the Q'-curvature, C. R. Math. Acad. Sci. Paris, 354(4):407–410, 2016.
    Announcment of arXiv:1511.05013.
    Journal link.  arXiv preprint.

14. (with Sun-Yung Alice Chang) On fractional GJMS operators, Comm. Pure Appl. Math., 69(6):1017–1061, 2016.
    Journal link.  arXiv preprint.

15. A notion of the weighted σk-curvature for manifolds with density, Adv. Math., 295:150–194, 2016.
    Journal link.  arXiv preprint.

16. A weighted renormalized curvature for manifolds with density, Proc. Amer. Math. Soc., 145:4031–4040, 2017.
    Journal link.  arXiv preprint.

17. Some energy inequalities involving fractional GJMS operators, Anal. PDE, 10(2):253–280, 2017.
    Journal link.  arXiv preprint.

18. Boundary operators associated to the Paneitz operator, Indiana Univ. Math. J., 67(1):293–327, 2018.
    Journal link.  arXiv preprint.

19. (with Sean N. Curry and Vladimir S. Matveev) On the Lichnerowicz conjecture for CR manifolds with mixed signature, C. R. Math. Acad. Sci. Paris, 356(5):532–537, 2018.
    Journal link.  arXiv preprint.

20. (with Yi Wang) Boundary operators associated to the σk-curvature, Adv. Math., 337:83–106, 2018.
    Journal link.  arXiv preprint.

21. (with Yi Wang) A Dirichlet principle for the k-Hessian, J. Funct. Anal., 275(11):2895–2916, 2018.
    Journal link.  arXiv preprint.

22. (with Chin-Yu Hsiao and Paul Yang) Extremal metrics for the Q'-curvature, J. Eur. Math. Soc., 21(2):585–626, 2019.
    Journal link. arXiv preprint.

23. (with Jih-Hsin Cheng and Paul Yang) An integral formula for the Q-prime curvature in 3-dimensional CR geometry, Proc. Amer. Math. Soc., 149:1577–1586, 2019.
    Journal link.  arXiv preprint.

24. The weighted σk-curvature of a smooth metric measure space, Pacific J. Math., 299(2):339–399, 2019.
    Journal link.  arXiv preprint.

25. (with Ana Claudia Moreira and Yi Wang) Nonuniqueness for a fully nonlinear boundary Yamabe-type problem via bifurcation theory, Calc. Var. PDE, 58:106, 2019.
    Journal link.  arXiv preprint.

26. (with Yueh-Ju Lin and Wei Yuan) Conformally variational Riemannian invariants, Trans. Amer. Math. Soc., 371:8217–8254, 2019.
    Journal link.  arXiv preprint.

27. (with Rod Gover) The P'-operator, the Q'-curvature, and the CR tractor calculus, Ann. Sc. Norm. Super. Pisa Cl. Sci., 20(2):565–618, 2020.
    Journal link. arXiv preprint.

28. Sharp weighted Sobolev trace inequalities and fractional powers of the Laplacian, J. Funct. Anal., 279(4):108567, 2020.
    Journal link.  arXiv preprint.

29. (with Yi Wang) Towards a fully nonlinear sharp Sobolev trace inequality, J. Math. Study, 53:402–435, 2020.
    Journal link.  arXiv preprint.

30. The Frank–Lieb approach to sharp Sobolev inequalities, Commun. Contemp. Math., 23(3):2050015, 2021.
    Journal link.  arXiv preprint.

31. (with Paul Yang) The Lichnerowicz–Obata theorem for the Kohn Laplacian in three dimensions, Adv. Math., 381:107618, 2021.
    Journal link.  arXiv preprint.

32. (with Weiyu Luo) Boundary operators associated to the sixth-order GJMS operator, Int. Math. Res. Not., 14:10600–10653, 2021.
    Journal link.  arXiv preprint.

33. An interesting family of conformally invariant one-forms in even dimensions, Diff. Geo. Appl., 82:101872, 2022.
    Journal Link,  arXiv preprint.

34. (with Yueh-Ju Lin and Wei Yuan) Some constructions of formally self-adjoint conformally covariant polydifferential operators, Adv. Math., 401:108312, 2022.
    Journal Link, arXiv preprint.

35. (with Yuya Takeuchi) I'-curvatures in higher dimensions and the Hirachi conjecture, J. Math. Soc. Japan. Advance Publication, July 2022.
    Journal Link, arXiv preprint.

36. Global obstructions to conformally Einstein metrics in dimension six, New York J. Math., 23:1085–1098, 2022.
    Journal Link, arXiv preprint.

37. (with Ayush Khaitan) The weighted ambient metric, SIGMA 18:086, 21 pages, 2022.
    Journal Link, arXiv preprint.

38. Some Q-curvature operators on five-dimensional pseudohermitian manifolds, J. Geom. Anal., 33(4):132, 2023.
    Journal Link, arXiv preprint.

39. (with Yueh-Ju Lin and Wei Yuan) Curved versions of the Ovsienko–Redou operators, Int. Math. Res. Not. IMRN 19:16904–16929, 2023.
    Journal Link, arXiv preprint.

40. (with Eric Chen, Yi Wang, Paul Yang, and Po-Lam Yung) The Neumann problem on the Clifford torus in S3, Adv. Nonlinear Stud. 23(1):ans-2022-072, 2023.

Journal Link, arXiv preprint.

41. A simple construction of the Rumin algebra, C. R. Math. Acad. Sci. Paris 361:1375–1382, 2023.

Journal Link, arXiv preprint.

42. (with Aaron J. Tyrrell) A sharp inequality for trace-free matrices with applications to hypersurfaces, Proc. Amer. Math. Soc.152(2):823–828, 2024.

Journal Link, arXiv preprint.

43. The bigraded Rumin complex via differential forms, Mem. Amer. Math. Soc., accepted.
    arXiv preprint.

Preprints

44. (with Peng Wu) A generalization of the Cai–Galloway splitting theorem to smooth metric measure spaces, arXiv:1307.0848.

45. (with Paul Yang) A CR invariant sphere theorem, arXiv:2204.02333.

46. (with C Robin Graham and Tzu-Mo Kuo) Extrinsic GJMS operators for submanifolds, arXiv:2306.11294.

47. The Obata-Vétois argument and its applications, arXiv:2309.12431.

48. (with Andrea Malchiodi) A factorization of the GJMS operators of special Einstein products and applications, arXiv:2310.12013.

49. (with João Henrique Andrade, Paolo Piccione, and Juncheng Wei) A general nonuniqueness result for Yamabe-type problems for conformally variational Riemannian invariants, arXiv:2310.15798.

50. (with Yueh-Ju Lin, Cheikh Birahim Ndiaye, Stephen E. McKeown, and Paul Yang) A fourth-order Cherrier-Escobar problem with prescribed corner behavior on the half-ball, arXiv:2401.00937.

51. (with C Robin Graham, Tzu-Mo Kuo, Aaron J. Tyrrell, and Andrew Waldron) A Gauss-Bonnet formula for the renormalized area of minimal submanifolds of Poincaré-Einstein manifolds, arXiv:2403.16710.

52. (with Pak Tung Ho) Deformations of the scalar curvature of a partially integrable pseudohermitian manifold, arXiv:2404.07002.

53. (with Ayush Khaitan, Yueh-Ju Lin, Aaron J. Tyrrell, and Wei Yuan) Computing renormalized curvature integrals on Poincaré-Einstein manifolds, arXiv:2404.11319.

54. (with Zetian Yan) Formal self-adjointness of a family of conformally invariant bidifferential operators, arXiv:2405.09532.