@inproceedings{687c867b26c64ccc951c29dbd722bb0a,
title = "Optimal Riemannian metric for a volumorphism and a mean ergodic theorem in complete global Alexandrov nonpositively curved spaces",
abstract = "In this paper we give a natural condition for when a volumorphism on a Riemannian manifold (M, g) is actually an isometry with respect to some other, optimal, Riemannian metric h. We consider the natural action of volumorphisms on the space M-mu(s), of all Riemannian metrics of Sobolev class H-s, s > n/2, with a fixed volume form mu. An optimal Riemannian metric, for a given volumorphism, is a fixed point of this action in a certain complete metric space containing M-mu(s) as an isometrically embedded subset. We show that a fixed point exists if the orbit of the action is bounded. We also generalize a mean ergodic theorem and a fixed point theorem to the nonlinear setting of complete global Alexandrov nonpositive curvature spaces.",
author = "Tony Liimatainen",
year = "2012",
doi = "10.1090/conm/584/11593",
language = "English",
isbn = "978-0-8218-9144-5",
series = "Contemporary Mathematics",
publisher = "American Mathematical Society",
pages = "163--178",
editor = "CL Aldana and M Braverman and B Lochum and CN Jimenez",
booktitle = "ANALYSIS, GEOMETRY AND QUANTUM FIELD THEORY",
address = "United States",
note = "International Conference on Analysis, Geometry and Quantum Field Theory ; Conference date: 26-09-2011 Through 30-09-2011",
}