Limit formulas for metric measure invariants and phase transition property
Limit formulas for metric measure invariants and phase transition property
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度量测度不变量和相变性质的极限公式
DOI：
10.1007/s00209-015-1447-2
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
R. Ozawa and T. Shioya
中科院分区：
文献类型：
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作者：
Shioya;Takashi;Kobayashi Shimpei;Tokuji Araya;古畑仁;R. Ozawa and T. Shioya
我们将度量空间的可观测直径和分离距离推广到金字塔的可观测直径和分离距离，并证明了收敛金字塔序列的这些不变量的极限公式。我们得到极限公式的各种应用如下。给出了度量度量空间或金字塔序列的相变性质判据，并给出了具有相变性质的非紧型对称空间的一些例子。我们也给出了Funano和Shioya （Geom Funct Anal 23(3):888 - 936,2013）关于an- lsamvy族极限的一个定理的简单证明。
We generalize the observable diameter and the separation distance for metric measure spaces to those for pyramids, and prove some limit formulas for these invariants for a convergent sequence of pyramids. We obtain various applications of our limit formulas as follows. We have a criterion of the phase transition property for a sequence of metric measure spaces or pyramids, and find some examples of symmetric spaces of noncompact type with the phase transition property. We also give a simple proof of a theorem in Funano and Shioya (Geom Funct Anal 23(3):888–936, 2013) on the limit of an-Lévy family.