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Quasiflats with holes in reductive groups

Kevin Wortman
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Abstract

We give a new proof of a theorem of Kleiner-Leeb: that any quasi-isometrically embedded Euclidean space in a product of symmetric spaces and Euclidean buildings is contained in a metric neighborhood of finitely many flats, as long as the rank of the Euclidean space is not less than the rank of the target. A bound on the size of the neighborhood and on the number of flats is determined by the size of the quasi-isometry constants. Without using asymptotic cones, our proof focuses on the intrinsic geometry of symmetric spaces and Euclidean buildings by extending the proof of Eskin-Farb's quasiflat with holes theorem for symmetric spaces with no Euclidean factors.

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Kevin Wortman. 2009-02-26. Quasiflats with holes in reductive groups. https://doi.org/10.2140/agt.2006.6.91

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