# Möbius rigidity of invariant metrics in boundaries of symmetric spaces of rank-1

Platis, I D; Schroeder, Viktor (2017). Möbius rigidity of invariant metrics in boundaries of symmetric spaces of rank-1. Monatshefte fuer Mathematik, 183(2):357-373.

## Abstract

Let $\mathbf{H}^{\mathit{n}}_{K}$ denote the symmetric space of rank-1 and of non-compact type and let $\mathit{d}_\mathfrak{H}$ be the Korányi metric defined on its boundary. We prove that if $\mathit{d}$ is a metric on $\partial\mathbf{H}^{\mathit{n}}_{K}$ such that all Heisenberg similarities are $\mathit{d}$-Möbius maps, then under a topological condition d is a constant multiple of a power of $\mathit{d}_\mathfrak{H}$.

## Abstract

Let $\mathbf{H}^{\mathit{n}}_{K}$ denote the symmetric space of rank-1 and of non-compact type and let $\mathit{d}_\mathfrak{H}$ be the Korányi metric defined on its boundary. We prove that if $\mathit{d}$ is a metric on $\partial\mathbf{H}^{\mathit{n}}_{K}$ such that all Heisenberg similarities are $\mathit{d}$-Möbius maps, then under a topological condition d is a constant multiple of a power of $\mathit{d}_\mathfrak{H}$.

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