Abstract
For any rank 1 nonpositively curved surface , it was proved by Burns-Climenhaga-Fisher-Thompson that for any , there exists a unique equilibrium state for , where is the geometric potential. We show that as , the weak-* limit of is the restriction of the Liouville measure to the regular set.
Acknowledgments
The authors would like to thank Federico Rodriguez Hertz for bringing up this question and for suggesting improvements in the exposition. We are also grateful to the referee for many helpful comments and useful remarks.
Disclosure statement
No potential conflict of interest was reported by the author(s).