Publications

  1. On the H\"{o}rmander's estimate. Submitted (2024)
  2. On the manifolds with noncompact automorphism groups. Submitted (2023)
  3. (with Emil Straube) Diederich-Forn\ae ss index and global regularity in the $\overline{\partial}$-Neumann problem: domains with comparable Levi eigenvalues. Submitted (2022).
  4. The $\bar{\partial}$-Neumann problem and boundary integral equations. Internat. J. Math. 34 (2023), no.1, Paper No. 2350001, 19 pp.
  5. (with Yu Su and Zhaosheng Feng) Ground state solution of the thin film epitaxy equation. J. Math. Anal. Appl. 503 (2021), no. 2, Paper No. 125357, 28 pp.
  6. (with Andrew Raich) The complex Green operator with Sobolev estimates up to a finite order. Int. J. Math. 31 (2020), no. 14, 2050122.
  7. The Diederich--Forn\ae ss index and the regularities on the $\bar{\partial}$-Neumann problem, Indiana U. Math. J. 71 (2022), no. 4, 1371-1395.
  8. (with Phillip Harrington) The $\bar{\partial}$-Neumann operator with the Sobolev norm of integer orders, Comm. Partial Differential Equations 45 (2020), no. 10, 1435-1450.
  9. The PDE method on the Riemann mapping theorem, Handbook of complex variables (2021).
  10. The Diederich--Fornæss index II: for domains of trivial index, Adv. Math. 344 (2019), 289-310.
  11. The Diederich-Fornæss index I: for the non-trivial index, Adv. Math. 353 (2019), 776-801.
  12. (with Steven Krantz and Marco Peloso) Geometric Analysis on the Diederich-Fornæss Index, J. Korean Math. Soc. 55 (2018), no. 4, 897 - 921.
  13. Two applications of the Schwarz lemma, Pacific J. Math. 296 (2018), no. 1, 141 -153.
  14. On the domains with noncompact automorphism groups, J. Math. Anal. Appl. 465 (2017), no.2, 903 - 911.
  15. The intrinsic geometry on bounded pseudoconvex domains, J. Geom. Anal. 28 (2018), no. 2, 1728 - 1748.
  16. (with Angel Cano and Marlon López) The limit set for discrete complex hyperbolic groups, Indiana U. Math. J. 66 (2017), no. 3, 927 - 948.
  17. Analysis of orbit accumulation points and the Greene-Krantz conjecture, J. Geom. Anal. 27 (2017), no. 1, 726 - 745.
  18. Finite type domains with hyperbolic orbit accumulation points, J. Math. Anal. Appl. 415 (2014), no. 1, 314 - 324.
  19. Classical inequalities for the discrete spectrum of Schrödinger operators, Preprint (2009).