Pure and Applied Mathematics Quarterly
Volume 12 (2016)
Integral of distance function on compact Riemannian manifolds
Pages: 293 – 300
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