Stabilities of rough curvature dimension condition

Kazukawa, Daisuke; Ozawa, Ryunosuke; Suzuki, Nobuo

doi:10.2969/jmsj/81468146

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2020

2024

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Cited by 5 publications

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“…The study of the concentration and the weak topologies has been growing in recent years (see [2,[4][5][6][10][11][12][13][14][15]). In particular, we have obtained in [6,14,15] some nontrivial examples of weak convergent sequences, for example, spheres with the restriction of Euclidean norm, solid ellipses, (projective) Stiefel manifolds with the Frobenius norm, whose dimensions are unbounded.…”

Section: Introductionmentioning

confidence: 99%

Convergence of metric transformed spaces

Kazukawa¹

2020

Preprint

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We consider the metric transformation of metric measure spaces/pyramids. We clarify the conditions to obtain the convergence of the sequence of transformed spaces from that of the original sequence, and, conversely, to obtain the convergence of the original sequence from that of the transformed sequence, respectively. As an application, we prove that spheres and projective spaces with standard Riemannian distance converge to a Gaussian space and the Hopf quotient of a Gaussian space, respectively, as the dimension diverges to infinity.

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