Remarks on the actions of some groups on the product of Hadamard spaces

Abstract

For a product of Hadamard spaces $X=X_1\times X_2$ on which some group $G\subset Is(X_1)\times Is(X_2)$ acting, G. Link arXiv:1107.3755v1 introduced the growth rate ${\delta }_{\theta }$ of slope $\theta$ to construct a $G-$invariant $(b,\theta )$-density. First, we show that ${\delta }_{\theta }$ is continuous in the slope $\theta$ as the above group action with some mild condition. Second, we give a negative answer to a question raised by G. Link in \cite{1} in general. And further results about the question are discussed. In the end, we can extent the $(b,\theta )$-densities in some reasonable condition.

15pages. Comments are welcome!

References in corpus (1)

• Generalized Patterson-Sullivan measures for products of Hadamard spaces