Ionescu's theorem for higher rank graphs

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.

Removing Sources from Higher-rank Graphs

For a higher-rank graph Λ with sources we detail a construction that creates a row-finite higher-rank graph Λ that does not have sources and contains Λ as a subgraph. Furthermore, when Λ is row-finite the Cuntz-Krieger algebra of Λ, C(Λ) is a full corner of C(Λ), the Cuntz-Krieger algebra of Λ.

Erratum for the Degree Theorem in Higher Rank

The purpose of this erratum is to correct a mistake in the proof of Theorem 4.1 of

A prime geodesic theorem for higher rank II: singular geodesics