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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A Bishop-type inequality on metric measure spaces with Ricci curvature bounded below
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by Yu Kitabeppu PDF
Proc. Amer. Math. Soc. 145 (2017), 3137-3151 Request permission

Abstract:

We define a Bishop-type inequality on metric measure spaces with Riemannian curvature-dimension condition. The main result in this short article is that any $RCD$ spaces with the Bishop-type inequalities possess only one regular set in not only the measure theoretical sense but also the set theoretical one. As a corollary, the Hausdorff dimension of such $RCD^*(K,N)$ spaces is exactly $N$. We also prove that every tangent cone at any point on such $RCD$ spaces is a metric cone.
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Additional Information
  • Yu Kitabeppu
  • Affiliation: Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
  • MR Author ID: 1055218
  • Email: y.kitabeppu@gmail.com
  • Received by editor(s): April 6, 2016
  • Received by editor(s) in revised form: June 28, 2016, and August 14, 2016
  • Published electronically: January 6, 2017
  • Communicated by: Jeremy Tyson
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 3137-3151
  • MSC (2010): Primary 51F99; Secondary 53C20
  • DOI: https://doi.org/10.1090/proc/13517
  • MathSciNet review: 3637960