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Geometry and Topology of Manifolds pp 299–314Cite as

Concentration, Convergence, and Dissipation of Spaces

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 154))

Abstract

We survey some parts of Gromov’s theory of metric measure spaces [6, Sect. 3.\(\frac{1}{2}\)], and report our recent works [14–17], focusing on the asymptotic behavior of a sequence of spaces with unbounded dimension.

The author is partially supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science.

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References

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Author information

Authors and Affiliations

  1. Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan

    Takashi Shioya

Authors
  1. Takashi Shioya
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Correspondence to Takashi Shioya .

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Editors and Affiliations

  1. The University of Tokyo, Meguro-ku, Tokyo, Japan

    Akito Futaki

  2. Mathematical Institute, Tohoku University, Sendai,Aoba-ku, Japan

    Reiko Miyaoka

  3. School of Mathematical Sciences, Beijing Normal University, Beijing, China

    Zizhou Tang

  4. Chern Institute of Mathematics, Nankai University, Tianjin, China

    Weiping Zhang

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Shioya, T. (2016). Concentration, Convergence, and Dissipation of Spaces. In: Futaki, A., Miyaoka, R., Tang, Z., Zhang, W. (eds) Geometry and Topology of Manifolds. Springer Proceedings in Mathematics & Statistics, vol 154. Springer, Tokyo. https://doi.org/10.1007/978-4-431-56021-0_16

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