Pure and Applied Mathematics Quarterly

Volume 12 (2016)

Number 2

Integral of distance function on compact Riemannian manifolds

Pages: 293 – 300

DOI: https://dx.doi.org/10.4310/PAMQ.2016.v12.n2.a5

Author

Jianming Wan (School of Mathematics, Northwest University, Xi’an, China)

Abstract

In this paper we show that, under some curvature assumptions the integral of distance function on a compact Riemannian manifold is bounded below by the product of diameter, volume and a constant only depending on the dimension.

Keywords

curvature, diameter, volume

2010 Mathematics Subject Classification

Primary 53C20. Secondary 53C22.

Full Text (PDF format)

The author was supported by National Natural Science Foundation of China No. 11301416.

Received 8 October 2016

Published 9 February 2018