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Publications

Mathematical Publications

  1. The classification of CR maps from hyperquadrics into tubes over null cones of symmetric forms. preprint [With Hien Nguyen and Michael Reiter] arXiv: 2510.13252

  2. Holomorphic rational maps from a real hyperquadric in \(\mathbb{C}^3\) to a homogeneous 2-nondegenerate model in \(\mathbb{C}^4\), Proceedings of the American Mathematical Society, Volume 154, Number 9, September 2026, Pages 3795–3807 [With Michael Reiter] DOI: 10.1090/proc/17721

  3. On CR maps from the sphere into the tube over the future light cone II: Higher dimensions. Journal of Mathematical Analysis and Applications, to appear [With Michael Reiter] arXiv: 2406.16428

  4. Kazdan–Warner identities for \(Q\)- and \(Q'\)-curvatures on three-dimensional CR manifolds, Pure and Applied Mathematics Quarterly,  Volume 21, Number 4, 1453–1468, 2025 DOI: 10.4310/PAMQ.250402012928 | PDF

  5. On a nonhomogeneous heat equation on the complex plane. International Journal of Mathematics, Vol. 35, No. 14 (2024) Article No. 2450060 (15 pages) [With Tran Van Thuy and Pham Truong Xuan] DOI: 10.1142/S0129167X24500605 | arXiv: 2406.06895

  6. 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

  7. 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 | Paper

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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

  23. A family of compact strictly pseudoconvex hypersurfaces in \(\mathbb{C}^2\) 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

  24. 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

  25. 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

  26. 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

  27. 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

  28. 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

  29. 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

  30. 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

  31. 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

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

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