We prove that, under a semi-ampleness type assumption on the twisted canonical line bundle, the conical Kahler-Ricci flow on a minimal elliptic Kahler surface converges in the sense of currents to a generalized conica...We prove that, under a semi-ampleness type assumption on the twisted canonical line bundle, the conical Kahler-Ricci flow on a minimal elliptic Kahler surface converges in the sense of currents to a generalized conical Kahler-Einstein on its canonical model. Moreover, the convergence takes place smoothly outside the singular fibers and the chosen divisor.展开更多
We give an elementary proof to the asymptotic expansion formula of Rochon and Zhang(2012)for the unique complete Kahler-Einstein metric of Cheng and Yau(1980),Kobayashi(1984),Tian and Yau(1987)and Bando(1990)on quasi-...We give an elementary proof to the asymptotic expansion formula of Rochon and Zhang(2012)for the unique complete Kahler-Einstein metric of Cheng and Yau(1980),Kobayashi(1984),Tian and Yau(1987)and Bando(1990)on quasi-projective manifolds.The main tools are the solution formula for second-order ordinary differential equations(ODEs)with constant coefficients and spectral theory for the Laplacian operator on a closed manifold.展开更多
基金supported by the Science and Technology Development Fund(Macao S.A.R.),Grant FDCT/016/2013/A1the Project MYRG2015-00235-FST of the University of Macao
文摘We prove that, under a semi-ampleness type assumption on the twisted canonical line bundle, the conical Kahler-Ricci flow on a minimal elliptic Kahler surface converges in the sense of currents to a generalized conical Kahler-Einstein on its canonical model. Moreover, the convergence takes place smoothly outside the singular fibers and the chosen divisor.
基金supported by National Natural Science Foundation of China(Grant Nos.11331001 and 11871265)the Hwa Ying Foundation for its financial support and thanks Professor Jian Song for his invitation。
文摘We give an elementary proof to the asymptotic expansion formula of Rochon and Zhang(2012)for the unique complete Kahler-Einstein metric of Cheng and Yau(1980),Kobayashi(1984),Tian and Yau(1987)and Bando(1990)on quasi-projective manifolds.The main tools are the solution formula for second-order ordinary differential equations(ODEs)with constant coefficients and spectral theory for the Laplacian operator on a closed manifold.
