Abstract

The present paper is devoted to investigation of the isometry group of the Gromov-Hausdorff space, i.e., the metric space of compact metric spaces considered up to isometry and endowed with the Gromov-Hausdorff metric. The main goal is to present a complete proof of the following result by G. Lowther (2015): the isometry group of the Gromov-Hausdorff space is trivial.

Keywords: Gromov-Hausdorff space; Gromov-Hausdorff distance; compact metric spaces; isometry groups; Metric Geometry.

MSC: 53C23, 54E45, 51F99

Pages:  123$-$154     

Volume  71 ,  Issue  1-2 ,  2019