McShane's identity in rank one symmetric spaces

Cohomogeneity One Actions on Noncompact Symmetric Spaces of Rank One

We classify, up to orbit equivalence, all cohomogeneity one actions on the hyperbolic planes over the complex, quaternionic and Cayley numbers, and on the complex hyperbolic spaces CHn, n ≥ 3. For the quaternionic hyperbolic spaces HHn, n ≥ 3, we reduce the classification problem to a problem in quaternionic linear algebra and obtain partial results. For real hyperbolic spaces, this classificat...

Ford Fundamental Domains in Symmetric Spaces of Rank One

We show the existence of isometric (or Ford) fundamental regions for a large class of subgroups of the isometry group of any rank one Riemannian symmetric space of noncompact type. The proof does not use the classification of symmetric spaces. All hitherto known existence results of isometric fundamental regions and domains are essentially subsumed by our work.

Singular Integrals on Symmetric Spaces of Real Rank One

In this paper we prove a new variant of the Herz majorizing principle for operators defined by K-bi-invariant kernels with certain large-scale cancellation properties. As an application, we prove L p-boundedness of operators defined by Fourier multipliers which satisfy singular differential inequalities of the Hörmander-Michlin type. We also find sharp bounds on the L p-norm of large imaginary ...

Curvature Characterization and Classification of Rank-one Symmetric Spaces

A Unified Approach to Compact Symmetric Spaces of Rank One

A relatively simple algebraic framework is given, in which all the compact symmetric spaces can be described and handled without distinguishing cases. We also give some applications and further results.