Research

Research Interests

  • Entropic inequalities and diffusion semi-groups.
  • Convexity in functional analysis, probability and complex analysis.
  • Geometric and functional inequalities on Euclidean space and Riemannian (and sub-Riemannian) manifolds (Brunn-Minkowski inequality, Prékopa-Leindler inequality, Brascamp-Lieb inequality, Isoperimetric inequality, log-Sobolev inequality, Sobolev type inequalities, Adams inequality, Moser-Trudinger inequality, etc)
  • Optimal transportations of measure and applications.
  • Geometry of log-concave probabilities and convex bodies in high dimension.
  • Convex geometry and affine isoperimetric inequalities..
  • Some inequalities in Information theory.
  • Liouville type theorems for fractional elliptic and parabolic problems.

Preprints and articles in preparation

  1. Dimensional variance inequalities on Riemannian manifolds with boundary, In preparation.
  2. Sharp Sobolev inequality on the Heisenberg type groups, In preparation.
  3. Valuations on Sobolev space W^{1,p}(\mathbb{R}^n), p > 1, work in progress.
  4. The sharp higher order Hardy–Rellich type inequalities on the homogeneous groups, preprint. (arXiv link)
  5. Sharp weighted anisotropic isoperimetric and Gagliardo–Nirenberg inequalities in \mathbb R^N, in preparation.
  6. The sharp Hardy–Sobolev type inequalities on the homogeneous groups and their stability version, in preparation.
  7. General Euclidean and affine Sobolev inequalities via rearrangement, in preparation.
  8. Extremal functions for sharp Hardy–Adams inequality for bi-Laplacian on hyperbolic space of dimension four, in preparation.
  9. Sharp Adams inequality in the fractional Sobolev–Slobodeckij spaces, in preparation.
  10. Sharp Adams inequality with the logarithmic weights, preprint.
  11. Extremal functions for improved Moser-Trudinger inequality of Adimurthi-Druet type under different norms in whole space, preprint.
  12. Sharp weighted Sobolev trace inequality on half space: a new proof, in preparation.
  13. The stability version of the sharp uncertainty principles, in preparation.

Submitted

  1. The Leray-Adams inequality, submitted. (arXiv link)
  2. The improved Moser–Trudinger inequalities in the hyperbolic spaces and their extremal functions, submitted.

Publications

  1. Ha Huy Bang, Nguyen Van Hoang, and Vu Nhat Huy, Best constants for the inequalities between equivalent norms in Orlicz spaces, Bull. Poli. Acad. Sci. Math, 59 (2) (2011) 165-174.(pdf) (link)
  2. Ha Huy Bang, Nguyen Van Hoang, and Vu Nhat Huy, Some properties of Orlicz-Lorentz spaces, Acta Math. Vietnam, 36 (2) (2011) 145-169. (pdf) (link)
  3. Keith Ball, and Van Hoang Nguyen, Entropy jumps for log-concave isotropic random vectors and spectral gap, Studia Math. 213 (1) (2012) 81-96. (pdf) (link)
  4. Van Hoang Nguyen, Dimensional variance inequalities of Brascamp-Lieb type and a local approach to dimensional Prekopa’s theorem, J. Funct. Anal. 266 (2014), 931-955. (pdf) (link)
  5. Van Hoang Nguyen, A local proof of the dimensional Prékopa’s theorem, J. Math. Anal. Appl. 419 (2014) 20-27. (pdf) (link)
  6. Van Hoang Nguyen, Sharp weighted Sobolev and Gagliardo-Nirenberg inequalities on half spaces via mass transport and consequences, Proc. London Math. Soc. 111 (2015) 127-148. (arXiv link) (link)(pdf)
  7. Van Hoang Nguyen, Improved L_p-mixed volume inequality for convex bodies, J. Math. Anal. Appl. 431 (2015) 1045-1053. (pdf) (link)
  8. Van Hoang Nguyen, Some trace Hardy type inequalities and trace Hardy-Sobolev-Maz’ya type inequalities, J. Funct. Anal.,  270 (2016), 4117-4151.  (arXiv link) (link)(pdf)
  9. Van Hoang Nguyen, New approach to the affine Polya-Szego principle and the stability version of the affine Sobolev inequality, Adv. Math., 302 (2016), 1080-1110. (arXiv link) (link)
  10. Quoc Anh Ngo, and Van Hoang Nguyen, Sharp reversed Hardy-Littlewood-Sobolev inequality on  \mathbb{R}^n, Israel J. Math., 220 (2017), 189-223. (link)
  11. Van Hoang Nguyen, Orlicz-Lorentz centroid bodies, Adv. in Appl. Math., 92 (2018) 99-121.  (arXiv link) (link)
  12. Van Hoang Nguyen, Improved Moser-Trudinger inequality for functions with mean value zero in \mathbb R^n and its extremal functions, Nonlinear Analysis, 163 (2017) 127-145. (link)
  13. Quoc Anh Ngo, and Van Hoang Nguyen, Sharp reversed Hardy-Littlewood-Sobolev inequality on the half space \mathbb{R}^n_+, Int. Math. Res. Not. IMRN 2017,  no. 20, 6187-6230. (arXiv link) (link)
  14. Van Hoang Nguyen, Improved Moser-Trudinger type inequalities in the hyperbolic space \mathbb H^n, Nonlinear Analysis, 168 (2018) 67-80. (arXiv link) (link)
  15. Van Hoang Nguyen, The sharp Poincaré-Sobolev type inequalities in the hyperbolic spaces \mathbb H^n, J. Math. Anal. Appl., 462 (2018) 1570-1584. (arXiv link) (link)
  16. Van Hoang Nguyen, and Futoshi Takahashi, On a weighted Trudinger-Moser type inequality on the whole space and related maximizing problem, Differential Integral Equations, 31 (2018), no. 11-12, 785-806. (arXiv link)(link)
  17. Sharp Caffarelli–Kohn–Nirenberg inequalities on stratified Lie groups, Ann. Acad. Sci Fenn. Math., 43 (2018), no. 2, 1073-1083. (pdf) (link)
  18. Improved Moser–Trudinger inequality of Tintarev type in dimension n and the existence of its extremal functions, Ann. Global Anal. Geom., 54 (2018), no. 2, 237-256. (link)
  19. Maximizers for the variational problems associated with Sobolev type inequalities under constraints, Math. Ann., 372 (2018), no. 1-2, 229-255. (arXiv link) (link) (link only to read)
  20. Quoc Anh Ngo, Quoc Hung Phan, and Van Hoang Nguyen, A pointwise inequality for a biharmonic equation with negative exponent and related problems, Nonlinearity, 31 (2018), no. 12, 5484-5499. (arXiv link) (link)
  21. Weighted Finsler trace Hardy inequality on half spaces, J. Math. Anal. Appl., 474 (2019), no. 2, 1198-1212. (link)
  22. A simple proof of the Moment-Entropy inequalities, Adv. in Appl. Math., 108 (2019) 31-44. (link)
  23. Second order Sobolev type inequalities in the hyperbolic spaces, J. Math. Anal. Appl., 477 (2019) 1157-1181. (arXiv link) (link)
  24. Concentration–Compactness principle for the sharp Adams  inequalities in bounded domains and whole space \mathbb{R}^n, J. Differential Equations, 267 (2019), no. 7, 4448-4492. (arXiv link) (link)
  25. Extremal functions for the Moser-Trudinger inequality of Adimurthi-Druet type in W^{1,N}(\mathbb R^N), Commun. Contemp. Math., 21 (2019), no. 4, 1850023, 37 pp. (arXiv link) (link)
  26. Sharp constant for Poincaré-type inequalities in the hyperbolic space, Acta Math. Vietnam., 44 (2019), no. 3, 781-795. (with Quoc Anh Ngo) (arXiv link) (link) (link only to read)
  27. The sharp Gagliardo-Nirenberg-Sobolev inequality in quantitative form, J. Funct. Anal., 277 (2019), no. 7, 2179-2208. (arXiv link) (link)
  28. \Phi-entropy inequalities and asymmetric covariance estimates for convex measures, Bernoulli, 25 (2019), no. 4A, 3090-3108. (arXiv link)(pdf) (link)
  29. Remarks on the Moser-Trudinger type inequality with logarithmic weights in dimension N, Proc. Amer. Math. Soc., 147 (2019), no. 12, 5183-5193. (pdf) (link)
  30. The weighted Moser–Trudinger inequalities of Adimurthi–Druet type in \mathbb R^N, Nonlinear Anal.,  (195) (2020) 111723. (link)
  31. Higher order Sobolev trace inequalities on balls revisited. J. Funct. Anal., 278 (2020), no. 7, 108414. (with Quoc Anh Ngo and Quoc Hung Phan) (arXiv link) (link)
  32. A supercritical Sobolev type inequality in higher order Sobolev spaces and related higher order elliptic problems, J. Differential Equations, 268 (2020), no. 10, 5996-6032. (with Quoc Anh Ngo) (arXiv link) (link)
  33. Supercritical Moser-Trudinger inequalities and related elliptic problems, Calc. Var and Partial Differential Equations, (2020) 59: 69. (with Quoc Anh Ngo) (link) (link only to read)
  34. Sharp Gagliardo-Nirenberg trace inequalities via mass transportation method and their affine versions, J. Geom. Anal., 30 (2020) 2132-2156. (arXiv link) (link) (link only ro read)
  35. The sharp affine L_2 Sobolev trace inequality and the affine energy in the fractional Sobolev spaces, Adv. in Appl. Math., 118 (2020) 102039. (link)
  36. The Hardy-Moser-Trudinger inequality via the transplantation of Green functions, Commun. Pure Appl. Anal., 19 (2020), no. 7,  3559-3574. (pdf) (link)
  37. The sharp Sobolev type inequalities in the Lorentz–Sobolev spaces in the hyperbolic spaces, J. Math. Anal. Appl., 490 (2020), no. 1, 124197. (arXiv link) (link)
  38. Improved singular Moser-Trudinger inequalities and their extremal functions, Potential Anal., 55 (2020) 55-88. (link) (link only to read)
  39. A simple proof of the Adams type inequalities in \mathbb R^{2m}, Discrete Cont. Dyn. Syst., 40 (2020), no. 10, 5755-5764. (link)
  40. Exhaustive existence and non-existence results for some prototype polyharmonic equations, J. Differential Equations, 269 (2020) 11621-11645. (with Quoc Anh Ngo, Quoc Hung Phan and Dong Ye) (link) (link, free until November 10, 2020)
  41. Extremals for the singular Moser-Trudinger inequality via n-harmonic transplantation, J. Differential Equations, 270 (2021) 843-882. (with Gyula Csato and Prosenjit Roy) (link) (link, free until November 10, 2020)
  42. Trudinger-Moser type inequalities with vanishing weights in the unit ball, J. Fourier Anal. Appl., 26 (2020) Article 77. (link) (link only to read)
  43. Sharp Adams-Moser-Trudinger type inequalities in the hyperbolic space, Rev. Mat. Iberoam., 36 (2020), no. 5, 1409-1467. (with Quoc Anh Ngo) (arXiv link) (link)
  44. Extremal functions for the sharp Moser–Trudinger type inequalities in whole space \mathbb R^N, J. Funct. Anal., 280 (2021), no. 3, 108833. (link) (link, free until December 24, 2020)
  45. New sharp Hardy and Rellich type inequalities on Cartan-Hadamard manifolds and their improvements, Proc. Roy. Soc. Edinburgh Sect. A., 150 (2020), no. 6, 2952-2981. (arXiv link) (link)
  46. A mass transportation proof for the sharp one-dimensional Gagliardo–Nirenberg inequalities, J. Math. Soc. Japan, 73 (2021), no 2, 633- 647. (pdf) (link)
  47. Liouville type theorems for fractional elliptic problems, Nonlinear Anal., 210 (2021) 112383 (with Anh Tuan Duong) (link) (link only to read)
  48. The thresholds of the existence of maximizers for the critical sharp singular Moser-Trudinger inequality under constraints, Math. Ann. 380 (2021), no. 3-4, 1933-1958 (link) (link only to read)
  49. Sharp Caffarelli-Kohn-Nirenberg inequalities on Riemannian manifolds: the influence of curvature, Proc. Roy. Soc. Edinburgh, Section A: Mathematics, 152 (2022), no. 1, 102-127. (arXiv link) (link)
  50. The sharp higher order Lorentz–Poincaré and Lorentz–Sobolev inequalities in the hyperbolic spaces, Ann. Mat. Pura Appl. (4), 200 (2021), no. 5, 2133-2153. (arXiv link) (link) (link only to read)
  51. Uniform lower bound and Liouville type theorem for  fractional Lichnerowicz equations, Bull. Aust. Math. Soc., 104 (2021), no. 3, 484-492. (with Anh Tuan Duong and Nguyen Thi Quynh) (link)
  52. Improved critical Hardy inequality and Leray-Trudinger type inequalities in Carnot groups, Ann. Fenn. Math., 47 (2022), no. 1, 121-138. (link)
  53. A Liouville type theorem for fractional elliptic equation with exponential nonlinearity, Mediterr. J. Math., 19 (2022), no. 2, Paper no. 91, 16pp. (with Anh Tuan Duong) (arXiv link) (link)
  54. Liouville type theorems for fractional parabolic problems, J. Dynam. Differential Equations, 35 (2023), no. 4, 3187-3200. (with Anh Tuan Duong) (link)
  55. On the lowest eigenvalue of the fractional Laplacian for the intersection of two domains, Bull. Aust. Math. Soc., 108 (2023), no. 2, 290-297. (with Anh Tuan Duong) (link)
  56. On the maximizing problem associated with critical Sobolev inequality under inhomogeneous constraints, Complex Var. Elliptic Equ., 68 (2023), no. 5, 681-700. (link)
  57. The sharp Hardy-Moser-Trudinger inequality in dimension n, Trans. Amer. Math. Soc., 377 (2024), no. 4, 2297-2315. (arxiv link) (link)
  58. A complete description of the asymptotic behavior at infinity of positive radial solutions to \Delta^2 u = u^\alpha in \mathbb R^n, to appear in Vietnam Journal of Mathematics. (with Quoc Anh Ngo and Quoc Hung Phan) (arXiv link)
  59. An optimal Hardy-Littlewood-Sobolev inequality on \mathbb R^{n-k}\times \mathbb R^n and its consequences, to appear in Journal d’Analyse Mathematiques. (with Quoc Anh Ngo and Quoc-Hung Nguyen) (arXiv link)
  60. On the stability estimate for the sharp second order uncertainty principle, Cal. Var. and PDE, 64 (2025), no. 4, Paper no. 129. (with Anh Tuan Duong) (link)
  61. On the sharp second order Caffarelli-Kohn-Nirenberg inequality, Ann. Fenn. Math., 50 (2025), no. 1, 275-286. (with Anh Tuan Duong) (link)
  62. The sharp Adams type inequalities in the hyperbolic space under the Lorentz-Sobolev norms, Cal. Var. PDE, 64, 210 (2025). (arXiv link) (link)
  63. A Concentration-compactness principle for the singular Adams inequalities and the singular polyharmonic equations with exponential critical growth, minor revision in Complex Variables and Elliptic Equations.
  64. Fractional Sobolev and Hardy-Littlewood-Sobolev inequalities, minor revision in Advances in Differential Equations. (with G. Jankowiak) (arXiv link)

My PhD thesis

“Inégalités fonctionnelles et convexité” sous la direction de Prof. Dario Cordero-Erausquin (UPMC). (pdf)

Jury: F. Barthe (Rapporteur), M. Fradelizi, I. Gentil, N. Gigli and B. Klartag (Rapporteur).

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