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My research interest lies between Several Complex Variables and CR geometry. The topics of my papers include the holomorphic mappings between CR manifolds, geometry of CR-umbilical points, eigenvalue problems for the Kohn-Laplacian, estimates for the Bergman kernels, immersions of CR manifolds, the Chern-Moser-Weyl tensor, CR maps between spheres and other homogeneous models, and the ∂-complex on Hermitian manifolds.
Kazdan-Warner type identities for CR \(Q\) and \(Q^{\prime}\) curvatures in three dimension. preprint (07/2022) 9 pages.
The CR umbilical locus of a real ellipsoid in \(\small\mathbb{C}^2\). preprint (under review) (05/2022) 16 pages, PDF | arXiv: 2205.03342.
On CR maps from the sphere into the tube over the future light cone. preprint (under review) (06/2021) 48 pages [With Michael Reiter] PDF | arXiv: 2106.07002.
Eigenvalues of the Kohn Laplacian and deformations of pseudohermitian structures on compact embedded strictly pseudoconvex CR manifolds, preprint (01/2019) pp. 19 [With Amine Aribi] PDF | arXiv: 1901.05881.
An upper bound for the first positive eigenvalue of the Kohn Laplacian on Reinhardt real hypersurfaces. Proceedings of the American Mathematical Society (accepted) [With Gian Maria Dall’Ara] DOI: 10.1090/proc/16077. PDF | arXiv: 2110.06704
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. arXiv: 2007.14764.
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). arXiv: 2008.04055 | MR4378569 | Zbl 0749.9472 |
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. arXiv: 1907.00834 | MR4398258 | Zbl 0749.2561 |
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. PDF. arXiv: 1903.12599 | MR4203322 | Zbl 0731.7363 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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.
2021: Some selected Topics in Complex Analysis and Complex Geometry, Vietnam Institute for Advanced Study in Mathematics, Hanoi, Vietnam (Online), December 9 - 10.
2021: DMV-ÖMG Jahrestagung 2021, §8 Funktionalanalysis, Reelle, Komplexe Analysis, Passau, Germany (Online), Sep 27 - Oct 1.
2021: Minisymposium “Complex Analysis and Geometry,” 8th European Congress of Mathematics, Portorož, Slovenia, June 20–26 (rescheduled from July 2020) [Abstract]
2019: Special Session on Complex Geometry and Dynamical Systems, Vietnam - USA Joint Mathematical Meeting, Quy Nhon, Vietnam, June 10–13.
2019: Complex Analysis, PDE, and their Applications, Hanoi, Vietnam, June 2–9.
2018: The 26th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, Fuzhou, China, July 9–13.
2018: Second Central European Complex Analysis Meeting, Vienna, Austria, April 12–14.
2017: Conference on Complex Geometry and PDEs, American University of Beirut, Lebanon, May 22–26.
2017: Analysis and Geometry in Several Complex Variables II, Texas A&M University at Qatar, Doha, Qatar, January 8–12.
2015: Workshop on “Several complex variables and CR geometry’’, ESI, Vienna, Austria, November 3–13.
2015: Summer Seminar, Vietnam National University, University of Science, Hanoi, Vietnam, August 6.- 2015: Analysis and Geometry in Several Complex Variables, Texas A&M University at Qatar, Doha, Qatar, January 4-8.
2014: Hayama Symposium of Several Complex Variables XVII, Hayama, Japan, July 19–22.
2012: French Mathematical Society and Vietnamese Mathematical Society joint Congress, Hue City, Vietnam, August 20–24.
2012: Southeast Analysis Meeting XXVIII, University of Alabama, AL, United States, March 9–10.
2011: RTG Workshop & Lecture Series, Topics in Several Complex Variables and CR Geometry, University of Michigan, United States, October 8–9.
2022: IBS Center for Complex Geometry, Several Complex Variables Seminar, Korea (Online), April 27.
2020: Universität zu Köln, Semiklassiche Analysis und Darstellungstheorie, Germany, January 21.
2019: Universität Wien, Complex Analysis Seminar, Austria, April 9.
2017: Universität Wien, Complex Analysis Seminar, Austria, October 31.
2016: Fujian Normal University, Fuzhou, Fujian, China, July 14.
2015: University of California, Riverside, CA, United States, January 22.
2013: University of California, Irvine, CA, United States, November 19.
2012: Rutgers University, Piscataway, NJ, United States, February 24.
2012: University of California, Irvine, CA, United States, February 21.
2011: University of California at San Diego, CA, United States, December 6.
© 2021 – 2022 Duong Ngoc Son, Ph.D.