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


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


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.


curvature, diameter, volume

2010 Mathematics Subject Classification

Primary 53C20. Secondary 53C22.

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

Received 8 October 2016

Published 9 February 2018