Publications | Recent Select Publications
Non-Existence of Black Hole Solutions for a Spherically Symmetric, Static Einstein-Dirac-Maxwell System, (with F. Finster and S.-T. Yau), Comm. Math. Phys., 205, 249-262.
The Interaction of Dirac Particles with Non-Abelian Gauge Fields and Gravity – Black Holes (with F. Finster and S.-T. Yau), Mich. Math. J., 47, 199-208.
Some Recent Progress in Classical General Relativity (with F. Finster and S.-T. Yau) , J. Math. Physics, 41, 3943-3963.
The Interaction of Dirac Particles with Non-Abelian Gauge Fields and Gravitation-Bound States (with F. Finster and S.-T. Yau), Nuclear Physics B, 584, 387-414.
Non-Existence of Time-Periodic Solutions of the Dirac Equation in a Reissner-Nordström Black Hole Background (with F. Finster and S.-T. Yau), J. Math. Physics 41, 2173-2194.
Non-Existence of Time-Periodic Solutions of the Dirac Equation in an Axisymmetric Black-Hole Geometry (with F. Finster, N. Kamran, and S.-T. Yau), Communications in Pure and Applied Mathematics 53, 902-929.
Shock-Wave Cosmology (with Blake Temple), Differential Equations and Mathematical Physics, AMS Studies in Advanced Mathematics (ed. by R. Weikard and G. Weinstein), 351-360.
Shock Wave Solutions of the Einstein Equations: A General Theory with Examples (with Blake Temple), Advances in the Theory of Shock Waves (ed. by H. Freisthüler and A. Szepessy), Birkhauser, (2001), 105-158.
Non-Formation of Vacuum States for the Compressible Navier-Stokes Equations (with D. Hoff), Communications in Mathematical Physics, 216, 255-276 (2001).
Absence of Stationary, Spherically Symmetric Black Hole Solutions for the Einstein-Dirac-Yang/Mills Equations with Complete Fermion Shells, (with F. Finster and S.-T. Yau), Advances in Theoretical and Mathematical Physics, Vol. 4, No. 2, (2002).
Shock-Wave Cosmology (with B. Temple), in: Hyperbolic Problems: Theory, Numerics, Applications, (ed. by. H. Freistüler and G. Warneche), Birhäuser Verlag, (2002), 861-867.
Shock-Wave Cosmology Inside a Black Hole (with B. Temple), Proc. Nat. Acad. Sci., 100, (2003), 11216-11218.
The Long-Time Dynamics of Dirac Particles in the Kerr-Newman Black-Hole Geometry (with F. Finster, N. Kamran, and S.-T. Yau), Adv. Theor. Math. Physics, 7, (2003) , 25-52.
Solving the Einstein Equations by Lipschitz Continuous Metrics: Shock Waves in General Relativity (with J. Groah and B. Temple), in: Handbook of Mathe-matical Fluid Dynamics, V. 2 (Ed. by S. Friedlander and D. Serre), Elsevier, (2003), 501-596.
Rotating Fluids with Self-Gravitation in Bounded Domains (with Tao Luo), Arch. Rat. Mech Anal., 173 (2004), 345-377.
Shock Wave Cosmology Inside a Black Hole II – the Case of Noncritical Expansion (with Blake Temple), J. Hyperbolic PDE’s, Vol. 1, (2004), 429-443.
Cosmology, Black Holes, and Shock Waves Beyond the Hubble Distance (with Blake Temple), Methods and Applications of Analysis, 11 (2004), 77-133.
The Interaction of Gravity with Other Force Fields, in: Proc. of 2nd InternationalCongress of Chinese Mathematicians, (ed. by C.S. Lim, L. Yang, and S.T. Yau), International Press, 9-23.
An Integral Representation for the Propagator for the Wave Equation in the Kerr Geometry, (with F. Finster, N. Kamran, and S.-T. Yau), Comm. Math. Physics, 260 (2005), 257-298.
Blowup of Smooth Solutions for Relativistic Euler Equations (with R. Pan), Comm. Math. Physics 282 (2006), 729-755.
How Inflation is Used to Solve the Flatness problem, (with Blake Temple), J. Hyp. P.D.E., 3, 375-386.
How Inflationary Spacetimes Can Evolve into Spacetimes of Finite Total Mass (with B. Temple), Methods and Applications of Analysis, 12, 451-464.
Decay of Solutions of the Wave Equation in the Kerr Geometry (with F. Finster, N. Kamran, and S.-T. Yau), Comm. Math. Phys., 264, 465-503.
A Shock Wave Refinement of the Friedman-Robertson-Walker Metric, (with Blake Temple), Encyclopedia of Physics, Elsevier.
BOOK: SHOCK WAVES AND THE INITIAL-VALUE PROBLEM IN GENERAL RELATIVITY (with B. Temple and J. Groah), Springer-Verlag, Springer Monographs in Mathematics.
A Time-Independent Energy Estimate for Outgoing Scalar Waves in the Kerr Geometry (with Felix Finster), J. Hyp. Diff. Eqns., 5, (2008), 221-255.
Nonlinear Dynamical Stability of Newtonian Rotating and Non-Rotating White Dwarfs and Rotating Supermassive Stars (with T. Luo), Comm. Math. Phys., 284, (2008), 425-457.
Existence and Nonlinear Stability of Rotating Star Solutions of the Compressible Euler-Poisson equations, (with Tao Luo), Arch. Rat. Mech. Anal, 191, (2009), 447-496.
Linear Stability of the Teukolsky Equation for Higher Spin in the Schwarzschild Geometry, (with Felix Finster), Adv. Theor. Math. Phys., 13, (2009), 71-110.
A Rigorous Treatment of Energy Extraction from a Rotating Black Hole, (with Felix Finster), Commun. Math. Phys 287, (2009), 829-847.
Linear Waves in the Kerr Geometry: A Mathematical Voyage to Black Hole Physics (with F. Finster, N. Kamran and S.T. Yau), Bull. AMS 46, (2009), 635-660.
A One Parameter Family of Expanding Wave Solutions of the Einstein Equations That Induces an Anomalous Acceleration Into the Standard Model of Cosmology, (with B. Temple), Proc. Nat. Acad. Sci, (USA) 16, (2009), 14213-14218.
Error Estimates for Approximate Solutions of the Riccati Equation with real or Complex Potentials, (with F. Finster), Arch. Rat. Mech. Anal. 16, (2009), 14213-14218
Asymptotic Behavior of Massless Dirac Waves in the Schwarzschild Geometry, (with C. Xie), Annales Institut Poincaré (to appear).