Publications

The following is a list of papers I have authored or collaborated on:

1. On CR maps from the sphere into the tube over the future light cone II: Higher dimensions. preprint [With Michael Reiter] arXiv: 2406.16428

2. On a nonhomogeneous heat equation on the complex plane. International Journal of Mathematics, (2024) [With Tran Van Thuy and Pham Truong Xuan] DOI: 10.1142/S0129167X24500605 | arXiv: 2406.06895

3. On CR maps between hyperquadrics and Winkelmann hypersurfaces. International Journal of Mathematics, Vol. 35, No. 12 (2024) Article No. 2450049 (19 pages) [With Michael Reiter] DOI: 10.1142/S0129167X24500496 | arXiv: 2404.16543

4. Kazdan–Warner identities for Q- and Q'-curvatures on three-dimensional CR manifolds, Pure and Applied Mathematics Quarterly, accepted for publication (2024) | PDF

5. On highly degenerate CR maps of spheres. The Journal of Geometric Analysis. Volume 34, article number 80, (2024) [With Giuseppe Della Sala, Bernhard Lamel, and Michael Reiter] DOI: 10.1007/s12220-023-01495-4 | Zbl 7796596 | arXiv: 2210.13525 | Paper |

6. The total Cartan curvature of Reinhardt surfaces. Journal of Mathematical Analysis and Applications. Volume 530, Issue 1, 1 February 2024, 127652 DOI: 10.1016/j.jmaa.2023.127652 | MR4630914 | Zbl 1528.32053 |

7. Eigenvalues of the Kohn Laplacian and deformations of pseudohermitian structures on CR manifolds. Journal of Spectral Theory. Volume 13, No. 1 (2023) 319–345 [With Amine Aribi] DOI: 10.4171/JST/443 | MR4620359 | Zbl 1528.32054 |

8. The CR umbilical locus of a real ellipsoid in \(\small\mathbb{C}^2\). Journal of Mathematical Analysis and Applications. Volume 518, Issue 1, 1 February 2023, 126701 DOI: 10.1016/j.jmaa.2022.126701 | arXiv: 2205.03342 | MR4489870 | MR4504613 | Zbl 1504.32093 |

9. An upper bound for the first positive eigenvalue of the Kohn Laplacian on Reinhardt real hypersurfaces. Proceedings of the American Mathematical Society. Volume 151, Number 1, January 2023, Pages 123–133 [With Gian Maria Dall’Ara] DOI: 10.1090/proc/16077 | arXiv: 2110.06704 | MR4504613 | Zbl 1517.32111 |

10. On CR maps from the sphere into the tube over the future light cone. Advances in Mathematics. Volume 410, Part A, 3 December 2022, 108743 [With Michael Reiter] DOI: 10.1016/j.aim.2022.108743 | MR4496726 | Zbl 1504.32045 |

11. The ∂-operator and real holomorphic vector fields. Pure and Applied Mathematics Quarterly. Volume 18, no. 3 (2022) 793 - 833 [With Friedrich Haslinger] DOI: PAMQ.2022.v18.n3.a1 | MR4461939 | Zbl 0756.5121 |

12. The holomorphic sectional curvature and “convex” real hypersurfaces in Kähler manifolds. Colloquium Mathematicum. Volume 168, no. 1 (2022) 149 - 170 DOI: 10.4064/cm8412-4-2021. Online First PDF (courtesy of IM PAN) | MR4378569 | Zbl 0749.9472 |

13. The CR Ahlfors derivative and a new invariant for spherically equivalent CR maps. Annales de l’Institut Fourier (Grenoble). Volume 71, no. 5 (2021) 2137 - 2167 [With Bernhard Lamel] DOI: 10.5802/aif.3438 | MR4398258 | Zbl 0749.2561 |

14. On the Chern-Moser-Weyl tensor of real hypersurfaces. Journal of the Mathematical Society of Japan. Volume 73, Number 1 (2021) 77 - 98 [With Michael Reiter] DOI: 10.2969/jmsj/82598259. Paper. arXiv: 1903.12599 | MR4203322 | Zbl 0731.7363 |

15. Semi-isometric immersions of CR manifolds into Kähler manifolds and applications. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5). Volume XXII.2 (2021) 957 - 987 DOI: 10.2422/2036-2145.201902_008 arXiv: 1901.07451 | MR4288678 | Zbl 7417794 |

16. The ∂-complex on weighted Bergman spaces on Hermitian manifolds. Journal of Mathematical Analysis and Applications. Volume 487, Issue 1 (2020) 123994 [With Friedrich Haslinger] DOI: 10.1016/j.jmaa.2020.123994. | MR4074193 | Zbl 1439.32013 |

17. Exponential decay of Bergman kernels on complete Hermitian manifolds with Ricci curvature bounded from below. Complex Variables and Elliptic Equations. Volume 65, Issue 12 (2020) 2086 - 2111 [With Franz Berger and Gian Maria Dall’Ara] DOI: 10.1080/17476933.2019.1691173 | MR4170198 | Zbl 0732.7104 |

18. CR-analogue of Siu-\(\small\partial\bar{\partial}\)-formula and applications to rigidity problem for pseudo-Hermitian harmonic maps. Proceedings of the American Mathematical Society. Volume 147, Number 12 (2019) 5141 - 5151 [With Song-Ying Li] DOI: 10.1090/proc/12997 | MR4021076 | Zbl 1429.32037 |

19. The Webster scalar curvature and sharp upper and lower bounds for the first positive eigenvalue of the Kohn-Laplacian on real hypersurfaces. Acta Mathematica Sinica, English Series, Volume 34, Issue 8 (2018) 1248 - 1258, a special issue in memory of Professor Qikeng Lu (1927-2015) [With Song-Ying Li] DOI: 10.1007/s10114-018-7415-0 | MR3843432 | Zbl 1404.32071 |

20. The sharp upper bounds for the first positive eigenvalue of the Kohn Laplacian on compact strictly pseudoconvex real hypersurfaces. Mathematische Zeitschrift. Volume 288, Issue 3-4 (2018) 949 - 963 [With Song-Ying Li and Guijuan Lin] DOI: 10.1007/s00209-017-1922-z | MR3778986 | Zbl 1396.32017 |

21. A family of compact strictly pseudoconvex hypersurfaces in \(\small\mathbb{C}^2\) without umbilical points. Mathematical Research Letters. Volume 25, Number 1 (2018) 75-84 [With Peter Ebenfelt and Dmitri Zaitsev] DOI: 10.4310/MRL.2018.v25.n1.a4 | MR3818615 | Zbl 1408.32033 |

22. The Schwarzian derivative and Möbius equation on strictly pseudoconvex CR manifolds. Communications in Analysis and Geometry. Volume 26, Number 2 (2018) 237 - 269 DOI: 10.4310/CAG.2018.v26.n2.a1 | MR3805160 | Zbl 1392.32016 |

23. Umbilical points on three dimensional strictly pseudoconvex CR manifolds. I. manifolds with U(1)-action. Mathematische Annalen. Volume 368, Issue 1 (2017) 537 - 560 [With Peter Ebenfelt] DOI: 10.1007/s00208-016-1439-5 | MR3651582 | Zbl 1375.32056 |

24. A new characterization of the CR sphere and the sharp eigenvalue estimate for the Kohn Laplacian. Advances in Mathematics, Volume 281 (2015) 1285 - 1305 [With Song-Ying Li and Xiaodong Wang] DOI: 10.1016/j.aim.2015.06.008 | MR3366867 | Zbl 1319.53032 |

25. Holomorphic mappings between pseudoellipsoids in different dimensions. Methods and Applications of Analysis, Volume 21, no. 3 (2014) 365 - 377 [With Peter Ebenfelt] DOI: 10.4310/MAA.2014.v21.n3.a6 | MR3286441 | Zbl 1302.32016 |

26. CR singular images of generic submanifolds under holomorphic maps, Arkiv för Matematik, Volume 52, no. 2 (2014) 301 - 327 [With Jiří Lebl, A. Minor, Ravi Shroff, and Yuan Zhang] DOI: 10.1007/s11512-013-0193-0 | MR3255142 | Zbl 1310.32040 |

27. Transversality of holomorphic mappings between real hypersurfaces in complex spaces of different dimensions. Illinois Journal of Mathematics, Volume 56, no. 1 (2012) 33 - 51 [With Peter Ebenfelt] DOI: 10.1215/ijm/1380287458 | MR3117016 | Zbl 1293.32043 |

28. CR transversality of holomorphic mappings between generic submanifolds in complex spaces. Proceedings of the American Mathematical Society, Volume 140, no. 5 (2012) 1729 - 1738 [With Peter Ebenfelt] DOI: 10.1090/S0002-9939-2011-11091-8 | MR2869157 | Zbl 1244.32011 |

29. A note on interpolation in the Lumer's Nevanlinna class. Indagationes Mathematicae, Volume 18, Issue 3 (2007) 447 - 453. DOI: 10.1016/S0019-3577(07)80033-4 | MR2373692 | Zbl 1143.32004 |

30. Remarks on subharmonic envelopes. Publicacions Matemàtiques (Barcelona), Volume 50, Issue 2 (2006) 447 - 456. DOI: 10.5565/PUBLMAT_50206_09 | MR2273669 | Zbl 1129.31001 |

For an almost complete list of my research preprints, see arXiv.