Limit formulas for metric measure invariants and phase transition property

Autor:	Ozawa, Ryunosuke, Shioya, Takashi
Rok vydání:	2014
Předmět:	Mathematics - Metric Geometry Mathematics - Differential Geometry 53C23
Druh dokumentu:	Working Paper
Popis:	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 by Funano-Shioya on the limit of an $N$-L\'evy family. Comment: 27 pages. arXiv admin note: text overlap with arXiv:1402.0611
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1402.6831 Zobrazit plný text záznamu View this record from Arxiv