A prime geodesic theorem for higher rank buildings

A prime geodesic theorem for higher rank spaces

A prime geodesic theorem for regular geodesics in a higher rank locally symmetric space is proved. An application to class numbers is given. The proof relies on a Lefschetz formula for higher rank torus actions.

A prime geodesic theorem for higher rank II: singular geodesics

The prime geodesic theorem for higher rank spaces

The prime geodesic theorem for regular geodesics in a higher rank locally symmetric space is proved. An application to class numbers is given. The proof relies on a Lefschetz formula that is based on work of Andreas Juhl.

The Degree Theorem in higher rank

The problem of relating volume to degree for maps between Riemannian manifolds is a fundamental one. Gromov’s Volume Comparison Theorem [Gr] gives such a relation for maps into negatively curved manifolds. In this paper we extend Gromov’s theorem to locally symmetric manifolds of nonpositive curvature. We derive this as a consequence of the following result, which we believe to be of independen...

Higher rank Einstein solvmanifolds

In this paper we study the structure of standard Einstein solvmanifolds of arbitrary rank. Also the validity of a variational method for finding standard Einstein solvmanifolds is proved.