Preprints and Publications of Xianghong Gong


o   (with H. Gaussier and A. Zimmer)  Smooth equivalence of families of strongly pseudoconvex domains, submitted, 31 pages.


o   (with L. Stolovitch) On neighborhoods of embedded complex tori, submitted, 23 pages.


o   On regularity of dbar-solutions on a_q domains with C^2 boundary in complex manifolds, submitted, 45 pages.


o   (with L. Stolovitch) A structure theorem for neighborhoods of compact complex manifolds,  J. Geom. Anal, (2024) 30 pages.


o   (with C. Gan) Global Newlander-Nirenberg theorem for domains with C2 boundary, Michigan Math. J.  (74)(2024), no. 2,  283-329.


o   (with L. Stolovitch) Equivalence of neighborhoods of embedded compact complex manifolds and higher codimension foliations, Arnold Math. J. 8 (2022) 61-145.


o   (with L. Lanzani) Regularity of a dbar-solution operator for strongly C-linearly convex domains with minimal smoothness, Elias M. Stein: In Memoriam. J. Geom. Anal, 31(2021), 6796-6818.


o   (with H. Gaussier) Smooth equivalence of deformations of domains in complex Euclidean spaces, Int. Math. Res. Not. IMRN (2020), no. 18, 5578-5610.


o    A Frobenius-Nirenberg theorem with parameter, J. reine angew. Math. 759 (2020), 101-159.


o    Hölder estimates for homotopy operators on strictly pseudoconvex domains with C2 boundary, Math. Ann. 374(2019), issues 1-2, 841-880.


o   (with L. Stolovitch) Real submanifolds of maximum complex tangent space at a CR singular point, II, J. Differential Geom. 112(2019), no. 1, 121-198.


o    (with K.-T. Kim) The dbar-equation on variable strictly pseudoconvex domains, Math. Z. 290(2018), issue 1-2, 111-144.


o    (with L. Stolovitch) Real submanifolds of maximum complex tangent space at a CR singular point, I, Invent. Math., 206(2016), no. 1, 293-377.


o    (with J. Lebl) Normal forms for CR singular codimension two Levi-flat submanifolds, Pacific J. Math. 275 (2015), no. 1, 115–165.


o    (with F. Bertrand) Dirichlet and Neumann problems for planar domains with parameter, Trans. Amer. Math. Soc. 366 (2014), no. 1, 159–217.


o    (with F. Bertrand and J.-P. Rosay) Common boundary values of holomorphic functions for two-sided complex structures, Michigan Math. J. 63 (2014), no. 2, 293-332.


o    Existence of divergent Birkhoff normal forms of Hamiltonian functions, Illinois J. Math. 56 (2012), no. 1, 85–94 (2013).


o    (with S. M. Webster) Regularity in the local CR embedding problem, J. Geom. Anal, 22(2012), no. 1, 261-293.


o    (with S. M. Webster) Regularity for the CR vector bundle problem II, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), (2011), no. 1, 129-191.


o    (with S. M. Webster) Regularity for the CR vector bundle problem I, Pure and Applied Mathematics Quarterly. 6 (2010), no.4, 983-998.


o    (with P. Ahern) Real analytic manifolds in Cn with parabolic complex tangents along a submanifold of codimension one, Ann. Fac. Sci. Toulouse Math. 18(2009), no.1, 1-64.


o    (with P. Ahern) Pairs of involutions of glancing hypersurfaces, Asian J. Math 11(2007), no. 1,  19-38.


o    (with J.-P. Rosay) Differential inequalities of continuous functions and removing singularities of Rado type for J-holomorphic maps, Math. Scand. 101(2007), no. 2, 293-319.


o    (with P. Ahern) Cusp-type singularities of real analytic curves in the complex plane, in Geometric Analysis of PDE and Several Complex Variables, Contemporary Mathematics 368(2005), 1-23.


o    (with P. Ahern) A complete classification for pairs of real analytic curves in the complex plane, J. Dynam. Control Systems, 11(2005), no. 1, 1-71,  & Erratum 13(2007), no. 2, 307-312.


o    Anti-holomorphically reversible holomorphic maps that are not holomorphically reversible, in Geometric function theory in several complex variables, World Sci. Publishing, River Edge, NJ, 2004. 151-164.


o    (with P. Cordaro) Normalization of complex-valued planar vector fields which degenerate along a real curve, Adv. Math. 184(2004), no.1, 89-118.


o    Existence of real analytic surfaces with hyperbolic complex tangent that are formally but not holomorphically equivalent to quadrics, Indiana Univ. Math. J. 53 (2004), no.1, 83-96.


o    Quantitative estimates for periodic points of reversible and symplectic holomorphic mappings, Math. Ann. 323(2002), no. 2, 227-257.


o    Conformal maps and non-reversibility of elliptic area-preserving maps, Math. Z. 237(2001), no. 2, 275-300.


o    Levi-flat invariant sets of holomorphic symplectic mappings, Ann. Inst. Fourier (Grenoble) 51(2001), no. 1, 151-208.


o    Conformal maps, monodromy transformations, and non-reversible Hamiltonian systems, Math. Res. Lett. 7 (2000), no. 4, 471-476.


o    (with D. Burns) Singular Levi-flat real analytic hypersurfaces, Amer. J. Math. 121(1999), no. 1, 23-53.


o    On totally real spheres in complex space, Math. Ann. 309(1997), no. 4, 611-623.


o    Unimodular invariants of totally real tori in Cn, Amer. J. Math. 119(1997), no. 1, 19-54.


o    Divergence of the normalization for real Lagrangian surfaces with complex tangents, Pacific J. Math. 176(1996), no. 2, 311-324.


o    Fixed points of elliptic reversible transformations with integrals, Ergodic Theory Dynam. Systems. 16(1996), no. 4, 683-702.


o    Integrable analytic vector fields with a nilpotent linear part, Ann. Inst. Fourier (Grenoble) 45(1995), no. 5, 1449-1470.


o    Real analytic submanifolds under unimodular transformations, Proc. Amer. Math. Soc. 123(1995), no. 1, 191-200.


o    On the convergence of normalizations of real analytic surfaces near hyperbolic complex tangents, Comment. Math. Helv., 69(1994), no. 4, 549-574.


o   Normal forms of real surfaces under unimodular transformations near elliptic complex tangents, Duke Math. J. 74(1994), no. 1, 145-157.


o   Divergence for the normalization of real analytic glancing hypersurfaces, Comm. Partial Differential Equations 19 (1994), no. 3-4, 643-654.


o    (with H. H. Chen) Singular directions and differential polynomials of meromorphic functions, A Chinese summary appears in Acta Math. Sinica 36 (1993), no. 5, 720. Acta Math. Sinica (N.S.) 8 (1992), no. 4, 424-431.


o    (with Y. X. Gu) On Hayman directions, Sci. Sinica, Ser. A 31(1988), no. 9, 1053-1064. 


o    The homogeneous differential polynomials and angular distribution of meromorphic functions. (Chinese) Acta Math. Sinica 30(1987), no. 3, 378-389.


o    (with X. R. Zhu) Homogeneous differential polynomials and normal families. (Chinese) Nanjing Daxue Xuebao Shuxue Bannian Kan, 3 (1986), no. 1, 43-49. 


      Research supported in part by NSF grants and a Simons collaboration grant.