# Jie Qing

Title | Professor, Chair, Mathematics Department |

Division | Physical & Biological Sciences |

Department | PBSci-Mathematics Department |

Phone | 831-459-3711 |

FAX | 831-459-4511 |

Office | McHenry Building Room #4149 |

Campus Mail Stop | Mathematics Department |

1156 High Street Santa Cruz, CA 95064 |

### 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.### Biography, Education and Training

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

### Selected Publications

- J. Qing: Hypersurfaces in hyperbolic space with support function, preprint 2012.
- J. Qing: Fractional conformal Laplacians and fractional Yamabe problems, accepted and to appear in Analysis and PDE 2012.
- J. Qing: Regularity and rigidity of asymptotically hyperbolic manifolds. Adv. Math. 230 (2012), no. 4-6, 2332–2363.
- J. Qing: Regularity of solutions to the liquid crystals systems in 2 and 3 dimensions. Nonlinearity 25 (2012), no. 2, 513–532.
- J. Qing: Norm inflation for incompressible magneto-hydrodynamic system. Adv. Differential Equations 16 (2011), no. 7-8, 725–746.
- J. Qing: Correspondences of hypersurfaces in hyperbolic Poincaré manifolds and conformally invariant PDEs. Proc. Amer. Math. Soc. 138 (2010), no. 11, 4109–4117.
- J. Qing: Spectral characterization of Poincaré-Einstein manifolds with infinity of positive Yamabe type. Int. Math. Res. Not. IMRN 2010, no. 9, 1720–1740.