论文标题
多能元的Chern-Ricci流动
Pluripotential Chern-Ricci Flows
论文作者
论文摘要
扩展了Guedj-Lu-Zeriahi和作者的紧凑型Kähler歧管发展的最新理论，我们定义和研究了多能解决方案，以对紧凑型Hermitian歧管的退化抛物线抛物面复杂的monge-ampère方程。在凯奇边界数据上的自然假设下，我们表明多能解决方案在时间上是半洞穴的，并且在空间中是连续的，并且这种解决方案是唯一的。我们还在密度的一些额外假设下建立了这种解决方案的部分规律性，并将其应用于证明弱Chern-Ricci流的存在和独特性，这是在具有对数末端奇点的复杂紧凑型品种上的存在。
Extending a recent theory developed on compact Kähler manifolds by Guedj-Lu-Zeriahi and the author, we define and study pluripotential solutions to degenerate parabolic complex Monge-Ampère equations on compact Hermitian manifolds. Under natural assumptions on the Cauchy boundary data, we show that the pluripotential solution is semi-concave in time and continuous in space and that such a solution is unique. We also establish a partial regularity of such solutions under some extra assumptions of the densities and apply it to prove the existence and uniqueness of the weak Chern-Ricci flow on complex compact varieties with log terminal singularities.
