论文标题
质量和渐近锥形Kähler指标的扩展
Mass and Expansion of Asymptotically Conical Kähler Metrics
论文作者
论文摘要
我们证明了对标量渐近式圆锥形kähler指标的扩展定理。考虑具有渐近型的AcKähler歧管，以具有复杂尺寸n的ricci-flatKähler度量锥。假设质量定义明确所需的较弱的衰减条件，则每个标量 - 贴量ackähler指标承认，膨胀是由公制锥的标准kähler公制给出的，并且领先的误差项为O（r^{2-2n}），系数仅根据ADM质量和其adm质量和压力。此外，在我们的环境中也可以证明Hein-Lebrun的大规模公式。作为一种应用，将在Ricci-FlatKähler锥的决议中讨论一个新版本的正质量定理。
We prove an expansion theorem on scalar-flat asymptotically conical Kähler metrics. Consider an AC Kähler manifold with asymptotic to a Ricci-flat Kähler metric cone with complex dimension n. Assuming the weak decay conditions required for the mass to be well-defined, then each scalar-flat AC Kähler metric admits an expansion that the main term is given by the standard Kähler metric of the metric cone and the leading error term is of O(r^{2-2n}) with coefficient only depending on the ADM mass and its dimension. Besides, the mass formula by Hein-LeBrun also can be proved in our setting. As an application, a new version of the positive mass theorem will be discussed in the cases of the resolutions of the Ricci-flat Kähler cones.
