## Journal of the Mathematical Society of Japan

### Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below, III

#### Abstract

This article is the third in a series of our investigation on a complete non-compact connected Riemannian manifold M. In the first series [KT1], we showed that all Busemann functions on an M which is not less curved than a von Mangoldt surface of revolution $M ˜$ are exhaustions, if the total curvature of $M ˜$ is greater than π. A von Mangoldt surface of revolution is, by definition, a complete surface of revolution homeomorphic to R2 whose Gaussian curvature is non-increasing along each meridian. Our purpose of this series is to generalize the main theorem in [KT1] to an M which is not less curved than a more general surface of revolution.

#### Article information

Source
J. Math. Soc. Japan, Volume 64, Number 1 (2012), 185-200.

Dates
First available in Project Euclid: 26 January 2012

https://projecteuclid.org/euclid.jmsj/1327586979

Digital Object Identifier
doi:10.2969/jmsj/06410185

Mathematical Reviews number (MathSciNet)
MR2836657

Zentralblatt MATH identifier
1246.53055

#### Citation

KONDO, Kei; TANAKA, Minoru. Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below, III. J. Math. Soc. Japan 64 (2012), no. 1, 185--200. doi:10.2969/jmsj/06410185. https://projecteuclid.org/euclid.jmsj/1327586979

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