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Boju–Funar type theorems via $m$ -Bakry–Émery and $m$ -modified Ricci curvatures

Homare Tadano

Department of Mathematics, Faculty of Science Division I, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku, Tokyo 162-8601, Japan

Institute of Mathematics, Academia Sinica, 6F, Astronomy-Mathematics Building, No. 1, Sec. 4, Roosevelt Road, Taipei 106319, Taiwan

E-mail Address: tadano@rs.tus.ac.jp

E-mail Address: tadano@yamaguchi-u.ac.jp

E-mail Address: tadano-homare-mt@alumni.osaka-u.ac.jp

Current address: Department of Mathematics, Faculty of Science, Yamaguchi University, 1677-1 Yoshida, Yamaguchi, Yamaguchi 753-8512, Japan.

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https://doi.org/10.1142/S0129167X21500518Cited by:0 (Source: Crossref)

Abstract

We establish some Boju–Funar type compactness criteria for complete Riemannian manifolds via $m$ -Bakry–Émery and $m$ -modified Ricci curvatures assuming that $m$ -Bakry–Émery and $m$ -modified Ricci curvatures tend slowly to zero as the distance from a fixed point goes to infinity. Our results are generalizations of Cheeger–Gromov–Taylor type compactness criteria for complete Riemannian manifolds via $m$ -Bakry–Émery and $m$ -modified Ricci curvatures established by Y. Soylu and the author.

Keywords:

AMSC: 53C20, 53C21

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