Publications

Most of my papers can be found on the arXiv webpage.

PDE theory arising from conformal geometry

1. (with H. Chen) Sharp quantitative stability of the Yamabe problem, preprint, arXiv:2404.13961, 55 pages.

2. (with S. Jin) Weighted isoperimetric ratios and extension problems for conformal fractional Laplacians, preprint, arXiv:2310.9160, 53 pages.

3. (with M. Musso) Infinite-time blowing-up solutions to small perturbations of the Yamabe flow, Advances in Mathematics, 443 (2024), Article No. 109611, 77 pages.

4. (with M. Musso and J. Wei) Compactness of scalar-flat conformal metrics on low-dimensional manifolds with constant mean curvature on boundary, Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire, 38 (2021), 1763-1793. [Addendum]

5. (with M. Musso and J. Wei) A compactness theorem of the fractional Yamabe problem, Part I: the non-umbilic conformal infinity, Journal of the European Mathematical Society (JEMS), 23 (2021), 3017-3073. [Addendum]

6. Conformal metrics with prescribed fractional scalar curvature on conformal infinities with positive fractional Yamabe constants, Journal of Geometic Analysis, 31 (2021), 4287-4327.

7. (with S. Deng and A. Pistoia) Linear perturbations of the fractional Yamabe problem on the minimal conformal infinity, Communications in Analysis and Geometry, 29 (2021), 363-407.

8. (with W. Chen) Bubble-tower solutions to asymptotically critical nonlocal elliptic equations on conformal infinities, Journal of Differential Equations, 265 (2018), 5115-5155.

9. (with M. Musso and J. Wei) Existence theorems of the fractional Yamabe problem, Analysis and PDE, 11 (2018), 75–113.

10. (with M. Musso and J. Wei) A non-compactness result on the fractional Yamabe problem in large dimensions, Journal of Functional Analysis, 273 (2017), 3759-3830. [Supplement]

11. (with W. Chen and S. Deng) Clustered solutions to low-order perturbations of fractional Yamabe equations, Calculus of Variations and Partial Differential Equations, 56 (2017), Article No. 160, 29 pages.

12. (with A. Pistoia) Nodal solutions for a Yamabe type equation, Journal of Nonlinear and Convex Analysis, 18 (2017), 1361–1373, Dedicated to Professor Norimichi Hirano on the occasion of his 65th birthday.

13. (with W. Choi) On perturbations of the fractional Yamabe problem, Calculus of Variations and Partial Differential Equations, 56 (2017), Article No. 14, 46 pages.

Qualitative behaviors of solutions to elliptic equations/systems

1. (with S. Moon) Asymptotic analysis on positive solutions of the Lane-Emden system with nearly critical exponents, Transactions of the American Mathematical Society, 376 (2023), 4835-4899.

2. (with R. L. Frank and A. Pistoia) Non-degeneracy for the critical Lane-Emden system, Proceedings of the American Mathematical Society, 149 (2021), 265-278. (This supersedes the previous paper `A perturbative approach to non-degeneracy of the Lane-Emden system' written with A. Pistoia.)

3. (with W. Choi) Asymptotic behavior of least energy solutions to the Lane-Emden system near critical hyperbola, Journal de Mathématiques Pures et Appliquées, 132 (2019), 398–456.

4. (with W. Choi) Minimal energy solutions to the fractional Lane-Emden system: Existence and singularity formation, Revista Matemática Iberoamericana, 35 (2019), 731–766.

5. (with W. Choi) Classification of finite energy solutions to the fractional Lane-Emden-Fowler equations with slightly subcritical exponents, Annali di Matematica Pura ed Applicata, 196 (2017), 269–308.

6. (with W. Choi and K. Lee) Qualitative properties of multi-bubble solutions for nonlinear elliptic equations involving critical exponents, Advances in Mathematics, 298 (2016), 484–533.

7. (with W. Choi and K. Lee) Asymptotic behavior of solutions for nonlinear elliptic problems with the fractional Laplacian, Journal of Functional Analysis, 266 (2014), 6531–6598.

Construction of bubbling solutions for elliptic equations/systems

1. (with S. Jin) Coron's problem for the critical Lane-Emden system, Journal of Functional Analysis, 285 (2023), Article No. 110077, 52 pages.

2. (with A. Pistoia) Multiple blowing-up solutions to critical elliptic systems in bounded domains, Journal of Functional Analysis, 281 (2021), Article No. 109203, 58 pages.

3. (with A. Pistoia) Supercritical problems in domains with thin toroidal holes, Discrete and Continuous Dynamical Systems - Series A, 34 (2014), 4671–4688.

4. (with J. Byeon and A. Pistoia) Existence of clustering high dimensional bump solutions of superlinear elliptic problems on expanding annuli, Journal of Functional Analysis, 265 (2013), 1955–1980.

5. (with A. Pistoia) Boundary towers of layers for some supercritical problems, Journal of Differential Equations, 255 (2013), 2302–2339.

6. (with A. Pistoia) Clustered boundary layer sign changing solutions for a supercritical problem, Journal of the London Mathematical Society, 88 (2013), 227–250.

Pure variational methods

1. (with O. Kwon and Y. Lee) Solutions with a prescribed number of zeros for nonlinear Schrödinger systems, Nonlinear Analysis, 86 (2013), 74–88.

2. On vector solutions for coupled nonlinear Schrödinger equations with critical exponents, Communications on Pure and Applied Analysis, 12 (2013), 1259–1277.

3. (with J. Seok) On nodal solutions of the nonlinear Schrödinger-Poisson equations, Communications in Contemporary Mathematics, 14 (2012), 1250041, 16 pages.