# Publications

Preprints

1. Dimensional variance inequalities on Riemannian manifolds with boundary, In preparation.
2. Sharp Sobolev inequality on the Heisenberg type groups, In preparation.
3. The sharp Gagliardo-Nirenberg-Sobolev inequality in quantitative form, submitted. (arXiv link)
4. Stability results for Gagliardo-Nirenberg-Sobolev inequality via mass transport, In preparation.
5. Valuations on Sobolev space $W^{1,p}(\mathbb{R}^n), p > 1$, work in progress.
6. Higher order Sobolev trace inequalities. In preparation. (with Quoc Anh Ngo and Quoc Hung Phan)
7. A pointwise inequality for a biharmonic equation with negative exponent and related problems, submitted. (arXiv link) (with Quoc Anh Ngo and Quoc Hung Phan)
8. The sharp higher order Hardy–Rellich type inequalities on the homogeneous groups, preprint. (arXiv link)
9. Sharp Caffarelli-Kohn-Nirenberg inequalities on Riemannian manifolds: the influence of curvature, preprint. (arXiv link)
10. The sharp Hardy-Moser-Trudinger inequality in dimension $n$, work in progress.
11. Exhaustive existence and non-existence results for some prototype polyharmonic equations, submitted. (with Quoc Anh NgoQuoc Hung Phan and Dong Ye) (arXiv link)
12. A complete description of the asymptotic behavior at infinity of positive radial solutions to $\Delta^2 u = u^\alpha$ in $\mathbb R^n$, submitted. (with Quoc Anh Ngo and Quoc Hung Phan) (arXiv link)
13. $\Phi$-entropy inequalities and asymmetric covariance estimates for convex measures, submitted. (pdf)
14. Second order Sobolev type inequalities in the hyperbolic spaces, submitted. (arXiv link)
15. Sharp weighted anisotropic isoperimetric and Gagliardo–Nirenberg inequalities in $\mathbb R^N$, in preparation.
16. The sharp Hardy–Sobolev type inequalities on the homogeneous groups and their stability version, in preparation.
17. A mass transportation proof for the sharp one-dimensional Gagliardo–Nirenberg inequalities, submitted. (pdf)
18. General Euclidean and affine Sobolev inequalities via rearrangement, in preparation.
19. Shadow system and the Orlicz–Brunn–Minkowski inequality, in preparation.
20. Extremal functions for sharp Hardy–Adams inequality for bi-Laplacian on hyperbolic space of dimension four, in preparation.

Unpublished Notes

1. A sharp Adams inequality in dimension four and its extremal functions. (arXiv link)
2. An improved Moser-Trudinger inequality involving the first non-zero Neumann eigenvalue with mean value zero in $\mathbb R^2$, preprint. (with Quoc Anh Ngo) (arXiv link)

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. 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. On a weighted Trudinger-Moser type inequality on the whole space and related maximizing problem, to appear in Differential and Integral Equations. (with Futoshi Takahashi) (arXiv link)
17. Improved Moser–Trudinger inequality of Tintarev type in dimension $n$ and the existence of its extremal functions, to appear in Annals of Global Analysis and Geometry. (link)
18. Extremal functions for the Moser-Trudinger inequality of Adimurthi-Druet type in $W^{1,N}(\mathbb R^N)$, to appear in Communications in Contemporary Mathematics. (arXiv link) (link)
19. Maximizers for the variational problems associated with Sobolev type inequalities under constraints, to appear in Mathematische Annalen. (arXiv link) (link) (link only to read)
20. Sharp constant for Poincaré-type inequalities in the hyperbolic space, to appear in Acta Mathematica Vietnamica. (with Quoc Anh Ngo) (arXiv link) (link) (link only to read)
21. Sharp Gagliardo-Nirenberg trace inequalities via mass transportation method and their affine versions, to appear in The Journal of Geometric Analysis. (arXiv link) (link) (link only ro read)
22. Sharp Caffarelli–Kohn–Nirenberg inequalities on stratified Lie groups, to appear in Annales Academiæ Scientiarum Fennicæ. Mathematica. (pdf)
23. Fractional Sobolev and Hardy-Littlewood-Sobolev inequalities, minor revision in Advances in Differential Equations. (with G. Jankowiak) (arXiv link)
24. New sharp Hardy and Rellich type inequalities on Cartan-Hadamard manifolds and their improvements, minor revision in Proceedings of the Royal Society of Edinburgh, Section A: Mathematics. (arXiv link) (title changed)
25. Concentration–Compactness principle for the sharp Adams  inequalities in bounded domains and whole space $\mathbb{R}^n$, minor revision in Journal of Differential Equations. (arXiv link)
26. Sharp Adams-Moser-Trudinger type inequalities in the hyperbolic space, minor revision in Revista Matematica Iberoamericana. (with Quoc Anh Ngo) (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).