论文标题
歧管的固有平坦稳定性，边界有汇聚和距离的边界
Intrinsic Flat Stability of Manifolds with Boundary where Volume Converges and Distance is Bounded Below
论文作者
论文摘要
Given a compact, connected, and oriented manifold with boundary $M$ and a sequence of smooth Riemannian metrics defined on it, $g_j$, we prove volume preserving intrinsic flat convergence of the sequence to the smooth Riemannian metric $g_0$ provided $g_j$ always measures vectors strictly larger than or equal to $g_0$, the diameter of $g_j$ is uniformly有限的，$ g_j $的体积收敛到$ g_0 $的音量，$ l^{\ frac {m-1} {2}}} $ contracence限制在边界上的指标收敛。审查了许多例子，证明并解释了这些假设背后的直觉。这些示例还表明，在这种情况下，统一，Lipschitz和Gromov-Hausdorff收敛不合适。我们的结果提供了一种新的严格方法，以证明正质量定理的固有平坦稳定性的某些特殊情况。
Given a compact, connected, and oriented manifold with boundary $M$ and a sequence of smooth Riemannian metrics defined on it, $g_j$, we prove volume preserving intrinsic flat convergence of the sequence to the smooth Riemannian metric $g_0$ provided $g_j$ always measures vectors strictly larger than or equal to $g_0$, the diameter of $g_j$ is uniformly bounded, the volume of $g_j$ converges to the volume of $g_0$, and $L^{\frac{m-1}{2}}$ convergence of the metrics restricted to the boundary. Many examples are reviewed which justify and explain the intuition behind these hypotheses. These examples also show that uniform, Lipschitz, and Gromov-Hausdorff convergence are not appropriate in this setting. Our results provide a new rigorous method of proving some special cases of the intrinsic flat stability of the positive mass theorem.
