科研项目:
1. 国家自然基金重点项目:凸几何偏微分方程及其应用(12231006),2023.01-2027.12,参与合作在研。
2. 浙江省自然基金探索项目:Grassmann流形的等周和逆等周问题研究(LY22A010001), 2022.1-2024.12主持,在研。
3. 河南省高等学校重点科研项目:等周和仿射等周相关问题研究(17A110022),2017.1-2018.12主持,已结项。
4. 国家自然科学基金(河南人才培养联合基金):Orlicz Minkowski 问题及相关极值理论(U1204102),2013.1-2015.12主持,已结项。
5. 国家自然科学基金:凸体的赋值理论与Busemann-Petty型问题(10971128),2010.1-2012.12,参与(第二),已结项。
6. 上海市教育委员会科研创新重点项目:现代凸几何分析及应用(09ZZ94),2009.1-2011.12,参与(第四),已结项。
近期发表的代表性论文:
[31] Q. Huang, and A.-J. Li, The Grassmannian Lp-sine Blaschke-Santalo inequality, J. Geom. Anal. 33 (2023), 317.
[30] Z.-X. Cao, Q. Huang, and A.-J. Li, On the Lp-sine moment-entropy inequality, Quaestiones Math. (2023), in press.
[29] Q. Huang, A.-J. Li, D. Xi, and D. Ye, On the sine polarity and the Lp-sine Blaschke-Santalo inequality, J. Funct. Anal. 283 (2022), 109571.
[28] A.-J. Li, Z.-X. Cao, and Q. Huang, A matrix form of Grassmannian Ball–Barthe inequality, Linear & Multilinear Algebra, 70 (2022), 6511-6522.
[27] A.-J. Li and Y.-M. Zhang, Lower dimensional ellipsoids of maximal volume in convex bodies, J. Math. Inequal. 16 (2022), 211-217.
[26] A.-J. Li and S.-T. Zhang, Sharp inequalities related to the functional Uj and some applications, Geom. Dedicata 213 (2021), 173–190.
[25] A.-J. Li, D. Xi, and Q. Huang, A Grassmannian Loomis-Whitney inequality and its dual, J. London Math. Soc. 101 (2020), 1219-1249.
[24] Q. Huang and A.-J. Li, The Lp Gagliardo-Nirenberg-Zhang inequality. Adv. Appl. Math. 113 (2020), 21 pp.
[23] A.-J. Li, Q. Huang, and D. Xi, New sine ellipsoids and related volume inequalities, Adv. Math. 353 (2019), 281-311.
[22] Y. Feng, Q. Huang, and A.-J. Li, On the reverse dual Loomis-Whitney inequality, Results in Math. 74 (2019), Art. 106.
[21] Q. Huang and A.-J. Li, Moment-entropy inequality for isotropic measures, Monatshefte Math. 187 (2018), 95–107.
[20] Q. Huang and A.-J. Li, A characterization of minimal Orlicz–Sobolev norms in the affine class, J. Math. Anal. Appl. 460 (2018), 703–713.
[19] Q. Huang, A.-J. Li and W. Wang, The complex Lp Loomis-Whitney inequality, Math. Inequal. Appl. 21 (2018), 369–383.
[18] A.-J. Li, Q. Huang, and D. Xi, Sections and projections of Lp-zonoids and their polars, J. Geom. Anal. 28 (2018), 427–447.
[17] A.-J. Li, Q. Huang, and D. Xi, Volume inequalities for sections and projections of Wulff shapes and their polars. Adv. Appl. Math. 91 (2017), 76–97.
[16] Q. Huang and A.-J. Li, The functional version of the Ball ineqaulity,Proc. Amer. Math. Soc. 145 (2017), 3531-3541.
[15] A.-J. Li, D. Xi, and G. Zhang, Volume inequalities of convex bodies from cosine transforms on Grassmann manifolds, Adv. Math. 304 (2017), 494-538.
[14] Q. Huang and A.-J. Li, On the Loomis-Whitney inequality for isotropic measures, Int. Math. Res. Notices 2017 (2017), 1641-1652.
[13] A.-J. Li and Q. Huang, The dual Loomis-Whitney inequality, Bull. London Math. Soc. 48 (2016), 676-690.
[12] A.-J. Li, Y. Lou, and Y. Ji, A Poincaré-type inequality on the Euclidean unit sphere, J. Math. Inequal. 10 (2016), 807–817.
[11] A.-J. Li and Q. Huang, The Lp Loomis-Whitney inequality, Adv. Appl. Math. 75 (2016), 94-115.
[10] Q. Huang and A.-J. Li,Optimal Sobolev norms in the affine class, J. Math. Anal. Appl. 436 (2016), 568-585.
[9] A.-J. Li, Isomorphic versions of reverse isoperimetric inequalities, Geom. Dedicata 179 (2015), 139-151.
[8] A.-J. Li, The generalization of Minkowski problems for polytopes, Geom. Dedicata 168 (2014),245-264.
[7] A.-J. Li and G. Leng, Extremal problems related to Gauss-John position, Acta Math. Sinica Enlish Series 28 (2012), 2527-2534.
[6] A.-J. Li and G. Leng, Mean width inequalities for isotropic measures, Math. Z. 270 (2012), 1089-1110.
[5] A.-J. Li, G. Wang, and G. Leng, An Extended Loomis-Whitney inequality for positive double John bases, Glasg. Math. J. 53 (2011) , 451-462.
[4] A.-J. Li and G. Leng, A new proof of Orlicz Busemann-Petty centroid inequality, Proc. Amer. Math. Soc. 139 (2011), 1473-1481.
[3] A.-J. Li and G. Leng, Brascamp-Lieb inequality for positive double John basis and its reverse , Science in China, Series A, 54 (2011), 399-410.
[2] A.-J. Li and C. Chen, Some completely monotonic functions involving the gamma and polygamma functions, J. Korean. Math. Soc. 45 (2008), 273-287.
[1] A.-J. Li, J. Yuan, and C. Chen, Monotonicity results for the polygamma functions, Math. Inequal. Appl. 11 (2008), 307-316.