A remark on the gromov convergence theorem

Yukio Otsu

doi:10.1090/S0002-9939-1990-0990431-7

A remark on the gromov convergence theorem

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Abstract

In [3] M. Gromov introduced the concept of convergence of Riemannian manifolds and he proved the convergence theorem. Since that time the theorem has been developed in detail (see [5], [7], [2]), and we know that it contains some interesting applications. Nevertheless there seems to be an inadequate way of applying the convergence theorem. The purpose of this paper is to present an example which shows that it is not correct.

Original language	English
Pages (from-to)	491-494
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	108
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1990-0990431-7
Publication status	Published - Feb 1990

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-1990-0990431-7

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title = "A remark on the gromov convergence theorem",

abstract = "In [3] M. Gromov introduced the concept of convergence of Riemannian manifolds and he proved the convergence theorem. Since that time the theorem has been developed in detail (see [5], [7], [2]), and we know that it contains some interesting applications. Nevertheless there seems to be an inadequate way of applying the convergence theorem. The purpose of this paper is to present an example which shows that it is not correct.",

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AB - In [3] M. Gromov introduced the concept of convergence of Riemannian manifolds and he proved the convergence theorem. Since that time the theorem has been developed in detail (see [5], [7], [2]), and we know that it contains some interesting applications. Nevertheless there seems to be an inadequate way of applying the convergence theorem. The purpose of this paper is to present an example which shows that it is not correct.

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A remark on the gromov convergence theorem

Abstract

All Science Journal Classification (ASJC) codes

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