Horospherical limit points of locally symmetric spaces

Grigori Avramidi; Dave Witte Morris

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arXiv · 1309.3554

Horospherical limit points of locally symmetric spaces

Grigori Avramidi·Dave Witte Morris

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Abstract

Suppose X/Gamma is an arithmetic locally symmetric space of noncompact type (with the natural metric induced by the Killing form of the isometry group of X), and let p be a point on the visual boundary of X. It was shown by T.Hattori that if each horoball based at p intersects every Gamma-orbit in X, then p is not on the boundary of any Q-split flat in X (where Q is the field of rational numbers). We prove the converse. (This was conjectured by W.H.Rehn in some special cases.) Furthermore, we prove an analogous result when Gamma is a nonarithmetic lattice.

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Grigori Avramidi, Dave Witte Morris. 2013-09-13. Horospherical limit points of locally symmetric spaces. https://arxiv.org/abs/1309.3554

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