Riemannian半球在其边界的单射包中是几乎校准的
The Riemannian hemisphere is almost calibrated in the injective hull of its boundary
AI总结：
本文在Riemannian圆周的单射包中构造恰当微分二形式，证明了以该圆周为边界的二维Ambrosio-Kirchheim流的Finsler质量下界，为Gromov填充面积猜想提供了正面证据。
摘要：
在Riemannian圆周的单射包中构造了一个恰当的微分二形式，其通过赋范平面上的内接Riemannian面积定义的comass范数，在该圆周所张开的开半球上的每一点处都是平稳的。由此，在任何度量空间中，以长度为$2π$的Riemannian圆周为边界的二维Ambrosio-Kirchheim可求长流的诱导Finsler质量具有下界，即$2π$加上与该半球等距副本的Hausdorff距离相关的二阶项。该估计适用于张成该圆周的所有有向Lipschitz曲面，无论其拓扑结构如何，从而为Gromov的填充面积猜想提供了正面证据。
英文摘要：
An exact differential two-form is constructed in the injective hull of the Riemannian circle, whose comass norm, defined via the inscribed Riemannian area on normed planes, is stationary at every point of the open hemisphere spanned by the circle. As a consequence, in any metric space, the induced Finsler mass of a two-dimensional Ambrosio-Kirchheim rectifiable current with boundary a Riemannian circle of length $2π$ admits a lower bound of $2π$ plus a second-order term in the Hausdorff distance to an isometric copy of the hemisphere. This estimate applies to all oriented Lipschitz surfaces spanning the circle, regardless of their topology, and thus offers positive evidence for Gromov's filling area conjecture.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
