Two theorems on the intersections of horospheres in asymptotically harmonic spaces
Differential Geometry
2022-06-28 v1
Abstract
We use Busemann functions to construct volume preserving mappings in an asymptotically harmonic manifold. If the asymptotically harmonic manifold satisfies the visibility condition, we construct mappings which preserve distances in some directions. We also prove that some integrals on the intersection of horospheres are independent of the differences between the values of the corresponding Busemann functions and we establish an upper bound of the volume of the intersection of two horospheres which is independent of the difference between values of corresponding Busemann functions.
Keywords
Cite
@article{arxiv.2206.12890,
title = {Two theorems on the intersections of horospheres in asymptotically harmonic spaces},
author = {Sinhwi Kim and JeongHyeong Park},
journal= {arXiv preprint arXiv:2206.12890},
year = {2022}
}
Comments
17 pages