论文标题
紧凑的黑森歧管上的黑森 - 科苏尔流的收敛性
Convergence of the Hesse-Koszul flow on compact Hessian manifolds
论文作者
论文摘要
我们研究了紧凑的Hessian歧管上Hesse-Koszul流的长时间行为。当第一个仿射Chern类是负面的时，我们证明该流量会收敛到独特的Hesse-Einstein度量。我们还得出了在任何紧凑的Hessian歧管上扭曲的Hesse-Koszul流动的收敛结果。这些结果为Cheng-Yau和Caffarelli-Viaclovsky以及Cheng-Yau，Delanoë和Caffarelli-Viaclovsky的真实Calabi Therorem以及Caffarelli-ViaClovsky的真实CALABI定理的存在提供了替代证明。
We study the long time behavior of the Hesse-Koszul flow on compact Hessian manifolds. When the first affine Chern class is negative, we prove that the flow converges to the unique Hesse-Einstein metric. We also derive a convergence result for a twisted Hesse-Koszul flow on any compact Hessian manifold. These results give alternative proofs for the existence of the unique Hesse-Einstein metric by Cheng-Yau and Caffarelli-Viaclovsky as well as the real Calabi theorem by Cheng-Yau, Delanoë and Caffarelli-Viaclovsky.
