论文标题
在曲率上方界限的度量空间中包装和加倍
Packing and doubling in metric spaces with curvature bounded above
论文作者
论文摘要
我们研究局部紧凑的，局部大地的完整，局部CAT（K）空间（GCBA（K）空间）。我们仅根据这些空间的维度来证明Croke型局部体积估计。我们表明，就自然措施而言，局部加倍条件意味着纯粹的差异性。然后，我们考虑在某个固定尺度上满足均匀填料条件的GCBA（K）空间，或在任意尺度上达到双倍条件，并证明了与尖锐的Gromov-Hausdorff收敛有关的几个紧凑性结果。最后，作为一种特殊的情况，我们研究了M^k综合物具有有界几何形状的收敛性和稳定性。
We study locally compact, locally geodesically complete, locally CAT(k) spaces (GCBA(k)-spaces). We prove a Croke-type local volume estimate only depending on the dimension of these spaces. We show that a local doubling condition, with respect to the natural measure, implies pure-dimensionality. Then, we consider GCBA(k)-spaces satisfying a uniform packing condition at some fixed scale or a doubling condition at arbitrarily small scale, and prove several compactness results with respect to pointed Gromov-Hausdorff convergence. Finally, as a particular case, we study convergence and stability of M^k-complexes with bounded geometry.
