Full publication list

In Differerntial Geometry and Geometric Analysis: 

1. A rigidity result for the product of spheres. Canad. Math. Bull. (2023), accepted.  Link  

2. (Joint with Julius Baldauf and Tang-Kai Lee) Parabolic frequency for the mean curvature flow. Int. Math. Res. Not. IMRN  (2024), no. 10, 8122-8136..  Link 

3. Existence results for the Einstein-scalar field Lichnerowicz equations on CR manifold in the null case. Differential Integral Equations 37 (2024), no. 9-10, 623-646.  Link 

4. (Joint with Jinwoo Shin) Slowly converging Yamabe-type flow on manifolds with boundary. Commun. Contemp. Math. 26 (2024), no. 3, Paper No. 2250072.  Link 

5. (Joint with Cheikh Birahim Ndiaye) Optimal control for the conformal CR sub-Laplacian obstacle problem. NoDEA Nonlinear Differential Equations Appl. 31 (2024), no. 3, Paper No. 35.  Link 

6. (Joint with Jinwoo Shin and Zetian Yan) Convergence rate of the weighted Yamabe flow. Diff. Geom. Appl. 93 (2024), Paper No. 102119.  Link 

7. (Joint with Yen-Chang Huang) The differential geometry of curves in B1×R. J. Geom. Anal. 34 (2024), no. 2, Paper No. 43.  Link 

8. (Joint with Juncheol Pyo) First eigenvalues of free boundary hypersurfaces in the unit ball along the inverse mean curvature flow. Diff. Geom. Appl. 93 (2024), Paper No. 102095.  Link

9. (Joint with Juncheol Pyo) Evolution of the first eigenvalue along the inverse mean curvature flow in space forms. J. Math. Anal. Appl. 532 (2024), no. 1, Paper No. 127980.  Link 

10. (Joint with Jinwoo Shin) Deformation of weighted scalar curvature. SIGMA Symmetry Integrability Geom. Methods Appl. 19 (2023), Paper No. 087.  Link

11. (Joint with Jinwoo Shin) Yamabe solitons with boundary. Ann. Mat. Pura Appl. (4) 202 (2023), no. 5, 2219–2253.  Link 

12.  (Joint with Jinwoo Shin and Zetian Yan) The weighted Yamabe flow with boundary. Comm. Pure Appl. Anal. 22 (2023), no. 8, 2590-2618.  Link 

13. (Joint with Jinwoo Shin) Weighted Yamabe solitons. Results Math. 78 (2023), no. 4, Paper No. 162.  Link  

14. (Joint with Juncheol Pyo) Sobolev inequality and isoperimetric inequality for submanifolds in a smooth metric measure space. Internat. J. Math. 34 (2023), no. 5, Paper No. 2350027, 21 pp.  Link 

15. (Joint with Jinwoo Shin) On the problem of prescribing weighted scalar curvature and the weighted Yamabe flow. Anal. Geom. Metr. Spaces 11 (2023), no. 1, agms–2022–0152.  Link 

16. Improved Lp-Folland-Stein-Sobolev inequality under constraints. Arch. Math. (Basel) 120 (2023), no.5, 521-532.  Link  

17. (Joint with Juncheol Pyo) Backward uniqueness for the inverse mean curvature flow.  Geom. Dedicata 41 (2023), no. 2, Paper No. 41, 6 pp.  Link 

18. Ancient caloric functions on pseudohermitian manifolds. J. Geom. Anal. 33 (2023), no. 2, Paper No. 41, 21 pp.  Link 

19. Einstein-scalar field Lichnerowicz equations on CR manifolds. Differential Integral Equations 36 (2022), no. 3-4, 161-204.  Link 

20. Results related to the transverse Yamabe problem. Internat. J. Math. 33 (2022), no. 14, Paper No. 2250091, 25 pp.  Link 

21. (Joint with Jinwoo Shin) Smooth Yamabe invariant with boundary. Ann. Global Anal. Geom. 62 (2022), no. 2, 413-435.  Link   

22. A note on the Sobolev trace inequality. Proc. Amer. Math. Soc. 150 (2022), no. 3, 1257-1267.  Link  

23. (Joint with Jinwoo Shin) Equivariant Yamabe problem with boundary. Calc. Var. Partial Differential Equations 61 (2022), no.1, Paper No. 38.  Link 

24. (Joint with Jinwoo Shin) Evolution of the Steklov eigenvalue along the conformal mean curvature flow. J. Geom. Phys. 173 (2022), Paper No. 104436.  Link 

25. (Joint with Rong Tang) Fractional Yamabe solitons and fractional Nirenberg problem. Comm. Pure Appl. Anal. 20 (2021), no. 9, 3215–3234.  Link

26.  Uniqueness results on CR manifolds. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 22 (2021), no. 2, 853-870.  Link 

27. (Joint with Jinwoo Shin) Chern-Yamabe problem and Chern-Yamabe soliton. Internat. J. Math. 32 (2021), no. 3, 2150016, 22 pp.  Link 

28. (Joint with Jih-Hsin Cheng and Hung-Lin Chiu) Connected sum of CR manifolds with positive CR Yamabe constant. J. Geom. Anal. 31 (2021), 298-311.  Link 

29. Results related to Chern-Yamabe flow. J. Geom. Anal. 31 (2021), 187-220.  Link 

30. (Joint with Junyeop Lee and Jinwoo Shin) The second generalized Yamabe invariant and conformal mean curvature flow on manifolds with boundary. J. Differential Equations 274 (2021), 251–305.  Link 

31. The Gauss-Bonnet-Chern mass under geometric flows. J. Math. Phys. 61 (2020), no. 11, 112501, 9 pp. Link 

32. (Joint with Seongtag Kim) CR Nirenberg problem and zero Wester scalar curvature. Ann. Global Anal. Geom. 58 (2020), 207–226.  Link 

33. On the Ricci-Bourguignon flow. Internat. J. Math. 31 (2020), no. 6, 2050044, 40 pp. Link 

34. (Joint with Kunbo Wang) CR Yamabe constant, CR Yamabe flow and its soliton. Nonlinear Anal. 199 (2020), 112043.  Link 

35. (Joint with Jinwoo Shin) On the cross curvature flow. Diff. Geom. Appl. 71 (2020), 101636.  Link

36. Prescribing Q-curvature on Sn in the presence of symmetry. Comm. Pure Appl. Anal. 19 (2020), 715-722.  Link 

37. (Joint with Hung-Lin Chiu) Global differential geometry of curves in three dimensional Heisenberg group and CR sphere. J. Geom. Anal. 29 (2019), 3438–3469.  Link 

38. (Joint with Hyunmo Koo) Evolution of the Steklov eigenvalue under geodesic curvature flow. Manuscripta Math. 159 (2019), 453-473. Link 

39. Prescribed mean curvature equation on the unit ball in the presence of reflection or rotation symmetry. Proc. Roy. Soc. Edinburgh Sect. A 149 (2019), 781-789.  Journal link  Link on arXiv.org 

40. (Joint with Weimin Sheng and Kunbo Wang) Convergence of the CR Yamabe flow. Math. Ann. 373 (2019), 743-830.  Link 

41. Prescribing the Q'-curvature in three dimension. Discrete Contin. Dyn. Syst. 39 (2019), 2285-2294.  Link 

42. Backwards uniqueness of the Yamabe flow. Diff. Geom. Appl. 62 (2019), 184-189. Link 

43. Conformal CR positive mass theorem. J. Geom. Anal. 28 (2018), 3477-3490.  Link 

44. First eigenvalues of geometric operators under the Yamabe flow. Ann. Global Anal. Geom. 54 (2018), 449-472. Link  Detailed version on arXriv.org

45. Bach flow. J. Geom. Phys. 133 (2018), 1-9. Link 

46. (Joint with Xuezhang Chen) Conformal curvature flows on compact manifold of negative Yamabe constant. Indiana U. Math. J. 67 (2018), 537-581.  Link 

47. (Joint with Xuezhang Chen and Liming Sun) Prescribed scalar curvature plus mean curvature flows in compact manifolds with boundary of negative conformal invariant. Ann. Global Anal. Geom. 53 (2018), 121-150.  Journal link  Detailed version on arXriv.org 

48. (Joint with Leyang Bo and Weimin Sheng) The k-Yamabe solitons and the quotient Yamabe solitons. Nonlinear Anal. 166 (2018), 181-195.  Link 

49. A characterization of the disk by eigenfunction of the Steklov eigenvalue. Manuscripta Math. 154 (2017), 297-307. Link 

50. (Joint with Seongtag Kim) The Yamabe problem on noncompact CR manifolds. Pacific J. Math. 285 (2016), 375-391. Link 

51. Prescribed Webster scalar curvature on S2n+1 in the presence of reflection or rotation symmetry. Bull. Sci. Math. 140 (2016), 506-518. Link 

52. Soliton to the fractional Yamabe flow. Nonlinear Anal. 139 (2016), 211-217.  Link 

53. The second CR Yamabe invariant. Pacific J. Math. 280 (2016), 371-400. Link

54. A note on compact CR Yamabe soliton. J. Geom. Phys. 94 (2015), 32-34. Link

55. Differentiable rigidity of hypersurface in space forms. Manuscripta Math. 146 (2015), 463-472. Link

56. Rigidity in a conformal class of contact form on CR manifold. C. R. Math. Acad. Sci. Paris 353 (2015), 167-172. Link

57. The Webster scalar curvature flow on CR sphere. Part II. Adv. Math. 268 (2015), 836-905.  Link 

58. The Webster scalar curvature flow on CR sphere. Part I. Adv. Math. 268 (2015), 758-835.  Link 

59. Almost Schur lemma for manifolds with boundary. Diff. Geom. Appl. 32 (2014), 97-112. Link

60. Results related to prescribing pseudo-Hermitian scalar curvature. Internat. J. Math. 24 (2013), pp29. Link

61. Results of prescribing Q-curvature on . Arch. Math. (Basel) 100 (2013), 85-93. Link

62. (Joint with H. Jacobowitz and P. Landweber) Optimality for totally real immersions and independent mappings of manifolds into . New York J. Math. 18 (2012), 463-477. Link 

63. Prescribed Q-curvature flow on Sn. J. Geom. Phys. 62 (2012), 1233-1261. Link 

64. The long time existence and convergence of the CR Yamabe flow. Commun. Contemp. Math. 14 (2012), pp50.  Link 

65. Prescribed curvature flow on surfaces. Indiana U. Math. J. 60 (2011), 1517-1542.  Link 

66. Q-curvature flow on Sn. Comm. Anal. Geom. 18 (2010), 791-820.  Link 

67. The structure of φ-stable minimal hypersurfaces in manifolds of nonnegative P-scalar curvature. Math. Ann. 348 (2010), 319-332.  Link 

68. Eigenvalue estimates for minimal hypersurfaces in hyperbolic space. Diff. Geom. Appl. 27 (2009), 104-108. Link

69. A remark on complete non-expanding Ricci solitons. Arch. Math. (Basel)  91 (2008), 284-288. Link

70. A first eigenvalue estimate for embedded hypersurfaces. Diff. Geom. Appl. 26 (2008), 273-276. Link

In Number Theory: 

1. Squares in (12 + m2) ⋯ (n2 + m2). Integers 9 (2009), 711-716.  Link 

In Graph Theory: 

1. The crossing number of K2,4,n. Ars Combin. 109 (2013), 527–537.  Link 

2. The projective plane crossing number of the circulant graph C(3k;{1,k}). Discuss. Math. Graph Theory 32 (2012), no. 1, 91–108.  Link 

3. The crossing number of K1,1,3,n. Ars Combin. 99 (2011), 461–471.  Link 

4. On Ramsey unsaturated and saturated graphs. Australas. J. Combin. 46 (2010), 13–18.  Link 

5. On the crossing number of some complete multipartite graphs. Util. Math. 79 (2009), 125–143.  Link 

6. The toroidal crossing number of K4,n. Discrete Math. 309 (2009), no. 10, 3238–3248.  Link 

7. The crossing number of K1,m,n. Discrete Math. 308 (2008), no. 24, 5996–6002.  Link 

8. A note on the total domination number. Util. Math. 77 (2008), 97–100.

9. The crossing number of K2,2,2,n. Far East J. Appl. Math. 30 (2008), no. 1, 43–69.

10. A proof of the crossing number of K3,n in a surface. Discuss. Math. Graph Theory 27 (2007), no. 3, 549–551.  Link 

11. The crossing number of C(3k+1;{1,k}). Discrete Math. 307 (2007), no. 22, 2771–2774.  Link 

12. On groupies in graphs. Australas. J. Combin. 38 (2007), 173–177.  Link 

13. The crossing number of K4,n on the real projective plane. Discrete Math. 304 (2005), no. 1-3, 23–33.  Link 

14. The crossing number of K1,5,n, K2,4,n and K3,3,n. Int. J. Pure Appl. Math. 17 (2004), no. 4, 491–515.