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Martin boundary for homogeneous riemannian manifolds of negative curvature at the bottom of the spectrum.

Ewa Damek, Andrzej Hulanicki, Roman Urban (2001)

Revista Matemática Iberoamericana

In this paper we treat noncoercive operators on simply connected homogeneous manifolds of negative curvature.

Metric Entropy of Homogeneous Spaces

Stanisław Szarek (1998)

Banach Center Publications

For a precompact subset K of a metric space and ε > 0, the covering number N(K,ε) is defined as the smallest number of balls of radius ε whose union covers K. Knowledge of the metric entropy, i.e., the asymptotic behaviour of covering numbers for (families of) metric spaces is important in many areas of mathematics (geometry, functional analysis, probability, coding theory, to name a few). In this paper we give asymptotically correct estimates for covering numbers for a large class of homogeneous...

Metrics with homogeneous geodesics on flag manifolds

Dimitri V. Alekseevsky, Andreas Arvanitoyeorgos (2002)

Commentationes Mathematicae Universitatis Carolinae

A geodesic of a homogeneous Riemannian manifold $(M = G / K, g)$ is called homogeneous if it is an orbit of an one-parameter subgroup of $G$ . In the case when $M = G / H$ is a naturally reductive space, that is the $G$ -invariant metric $g$ is defined by some non degenerate biinvariant symmetric bilinear form $B$ , all geodesics of $M$ are homogeneous. We consider the case when $M = G / K$ is a flag manifold, i.eȧn adjoint orbit of a compact semisimple Lie group $G$ , and we give a simple necessary condition that $M$ admits a non-naturally reductive...

Minimal cones and the spherical Bernstein prob-lem. III.

W.-Y. Hsiang, I. Sterling (1986)

Inventiones mathematicae

Moduli for spherical maps and minimal immersions of homogeneous spaces.

Toth, Gabor (2002)

Journal of Lie Theory