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Convex rank 1 subsets of Euclidean buildings (of type A 2)

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Abstract

For a Euclidean building X of type A 2, we classify the 0-dimensional subbuildings A of ∂ T X that occur as the asymptotic boundary of closed convex subsets. In particular, we show that triviality of the holonomy of a triple (of points of A) is (essentially) sufficient. To prove this, we construct new convex subsets as the union of convex sets.

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  1. Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresienstrasse 39, D-80333, Munich, Germany

    Andreas Balser

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  1. Andreas Balser
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Correspondence to Andreas Balser.

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Balser, A. Convex rank 1 subsets of Euclidean buildings (of type A 2). Geom Dedicata 131, 123–158 (2008). https://doi.org/10.1007/s10711-007-9221-1

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  • DOI: https://doi.org/10.1007/s10711-007-9221-1

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