Department/College/UnitPhysical & Biological Sciences Division

TitleChair, Distinguished Professor

AffiliationFaculty

Web SitePersonal

Primary Office LocationMcHenry Library
McHenry #4149

Mail StopMathematics Department

Biography, Education and Training

B.S., M.S., Peking University
Ph.D., University of California, Los Angeles

Summary of Expertise

Jie Qing works on conformal geometry, the AdS‑CFT correspondence, and most recently in general relativity. In conformal geometry, only the angle between two vectors can be measured but not the vector’s lengths. The AdS‑CFT correspondence relates the Riemannian or pseudo-Riemannian (general relativistic) geometry on one manifold to the conformal geometry of a manifold that bounds it. AdS‑CFT has roots going back about 30 years but became very popular in the last decade due to its relevance to string theory. Qing has some of the strongest uniqueness results available in AdS/CFT for conformal spheres.

Research Interests

Jie Qing is interested in nonlinear analysis, harmonic analysis, and partial differential equations (systems) with applications to differential geometry, complex geometry and mathematical physics. More specifically Jie Qing is working in the fields of conformal geometry, partial differential equations in conformal geometry, geometric problems arising from mathematical relativity. Currently Jie Qing is interested in developing mathematical foundation for AdS/CFT correspondence proposed in the promising theory of quantum gravity in Mathematical Physics.

Selected Publications

• Liu, Huajie; Ma, Shiguang; Qing, Jie; Zhong, Shuhui; On the asymptotic behavior of p-superharmonic functions at singularities, arXiv:2310.11610
• Liu, Huajie; Ma, Shiguang; Qing, Jie; Zhong, Shuhui; p-Laplace equations in conformal geometry, arXiv:2308.02468
• Ma, Shiguang; Qing, Jie; Linear potentials and applications in conformal geometry, arXiv:2209.02823
• Chang, Alice; Ge, Yuxin; JIn, Xiashang; Qing, Jie; Perturbation compactness and uniqueness for a class of conformally compact Einstein manifolds, Adv. Nonlinear Stud. 24 (2024), no. 1, 247 - 278.
• Chen, Jiaqi; Lu, Peng; Qing, Jie; Conformal Bach flow, Ann. Global Anal. Geom. 63 (2023), no. 2, Paper No. 19, 30 pp.
• Ma, Shiguang; Qing, Jie; On Huber-type theorems in general dimensions, Adv. Math. 395 (2022), Paper No. 108145, 37 pp.
• Ma, Shiguang; Qing, Jie; On  n-superharmonic functions and some geometric applications, Calc. Var. Partial Differential Equations 60 (2021), no. 6, 42 pp.
• Ma, Shiguang; Qing, Jie; Arsove-Huber theorem in higher dimensions. Geometric Analysis, 245–263, Progr Math., 333, Birkhauser/Springer, Cham, 2020, 245 - 263.
• Chang, Sun-Yung A.; Ge, Yuxin; Qing, Jie Compactness of conformally compact Einstein 4-manifolds II. Adv. Math. 373 (2020), 107325, 33 pp.
• Bonini, Vincent; Ma, Shiguang; Qing, Jie Hypersurfaces with nonnegative Ricci curvature in ℍn+1 . Calc. Var. Partial Differential Equations 58 (2019), no. 1, Paper No. 36, 14 pp.
•  Lu, Peng; Qing, Jie; Zheng, Yu Conformal Ricci flow on asymptotically hyperbolic manifolds. Sci. China Math. 62 (2019), no. 1, 157–170.
• Bonini, Vincent; Ma, Shiguang; Qing, Jie On nonnegatively curved hypersurfaces in ℍn+1. Math. Ann. 372 (2018), no. 3-4, 1103–1120.
• Bonini, Vincent; Qing, Jie; Zhu, Jingyong Weakly horospherically convex hypersurfaces in hyperbolic space. Ann. Global Anal. Geom. 52 (2017), no. 2, 201–212.
• Li, Tongzhu; Qing, Jie; Wang, Changping Möbius curvature, Laguerre curvature and Dupin hypersurface. Adv. Math. 311 (2017), 249–294.
• Li, Gang; Qing, Jie; Shi, Yuguang Gap phenomena and curvature estimates for conformally compact Einstein manifolds. Trans. Amer. Math. Soc. 369 (2017), no. 6, 4385–4413. 
• Qing, Jie; Yuan, Wei On scalar curvature rigidity of vacuum static spaces. Math. Ann. 365 (2016), no. 3-4, 1257–1277. 
• Bonini, Vincent; Espinar, José M.; Qing, Jie Hypersurfaces in hyperbolic space with support function. Adv. Math. 280 (2015), 506–548.
• Lu, Peng; Qing, Jie; Zheng, Yu A note on conformal Ricci flow. Pacific J. Math.268 (2014), no. 2, 413–434.
•  González, María del Mar; Qing, Jie Fractional conformal Laplacians and fractional Yamabe problems. Anal. PDE 6 (2013), no. 7, 1535–1576. 
• Qing, Jie; Yuan, Wei A note on static spaces and related problems. J. Geom. Phys. 74 (2013), 18–27. 
• Qing, Jie; Shi, Yuguang; Wu, Jie Normalized Ricci flows and conformally compact Einstein metrics. Calc. Var. Partial Differential Equations 46 (2013), no. 1-2, 183–211. 
• Liu, Xian-Gao; Qing, Jie Globally weak solutions to the flow of compressible liquid crystals system. Discrete Contin. Dyn. Syst. 33 (2013), no. 2, 757–788. 
• Qing, Jie Asymptotically hyperbolic manifolds and conformal geometry. Recent developments in geometry and analysis, 329–344, Adv. Lect. Math. (ALM), 23, Int. Press, Somerville, MA, 2012.
•  Dai, Mimi; Qing, Jie; Schonbek, Maria Asymptotic behavior of solutions to liquid crystal systems in ℝ3. Comm. Partial Differential Equations 37 (2012), no. 12, 2138–2164. 
• Hu, Xue; Qing, Jie; Shi, Yuguang Regularity and rigidity of asymptotically hyperbolic manifolds. Adv. Math. 230 (2012), no. 4-6, 2332–2363.
• Dai, Mimi; Qing, Jie; Schonbek, Maria Regularity of solutions to the liquid crystals systems in ℝ2 and ℝ3. Nonlinearity 25 (2012), no. 2, 513–532.
• Dai, Mimi; Qing, Jie; Schonbek, Maria E. Norm inflation for incompressible magneto-hydrodynamic system in B−1,∞∞. Adv. Differential Equations 16 (2011), no. 7-8, 725–746. 
• Bonini, Vincent; Espinar, José M.; Qing, Jie Correspondences of hypersurfaces in hyperbolic Poincaré manifolds and conformally invariant PDEs. Proc. Amer. Math. Soc. 138 (2010), no. 11, 4109–4117.
• Guillarmou, Colin; Qing, Jie Spectral characterization of Poincaré-Einstein manifolds with infinity of positive Yamabe type. Int. Math. Res. Not. IMRN 2010, no. 9, 1720–1740.