 

Grigori Avramidi and Dave Witte Morris
Horospherical limit points of finitevolume locally symmetric spaces
view print


Published: 
April 10, 2014 
Keywords: 
Horospherical limit point, locally symmetric space, Tits building, arithmetic group, Ratner's theorem 
Subject: 
53C35 (Primary); 20G30, 22E40 (Secondary) 


Abstract
Suppose X/Γ 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 ξ be a point on the visual boundary of X. T.Hattori showed that if each horoball based at ξ intersects every Γorbit in X, then ξ is not on the boundary of any Qsplit flat in X. We prove the converse. (This was conjectured by W.H.Rehn in some special cases.)
Furthermore, we prove an analogous result when Γ is a nonarithmetic lattice.


Author information
Grigori Avramidi:
Department of Mathematics, University of Chicago, Chicago, IL 60637
Current Address: Department of Mathematics, University of Utah,
Salt Lake City, UT 841120090
gavramid@math.utah.edu
Dave Witte Morris:
Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, Alberta, T1K6R4, Canada
Dave.Morris@uleth.ca

