论文标题
Kähler几何形状的直径估计值
Diameter estimates in Kähler geometry
论文作者
论文摘要
建立了Kähler指标的直径估计值，该指标仅需要熵结合，而在RICCI曲率上不需要下限。该证明是基于最新的Monge-Ampère方程$ l^\ Infty $估计值的PDE技术，其关键改进允许脱离编码形式的变性，严格大于一个。结果，当限制类别大，以及Calabi-yau歧管的特殊振动时，获得了Kähler-Icci流量和有限时间溶液的长期解决方案的直径边界。
Diameter estimates for Kähler metrics are established which require only an entropy bound and no lower bound on the Ricci curvature. The proof builds on recent PDE techniques for $L^\infty$ estimates for the Monge-Ampère equation, with a key improvement allowing degeneracies of the volume form of codimension strictly greater than one. As a consequence, diameter bounds are obtained for long-time solutions of the Kähler-Ricci flow and finite-time solutions when the limiting class is big, as well as for special fibrations of Calabi-Yau manifolds.
