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Convex rank 1 subsets of Euclidean buildings (of type $A_2$)

Andreas Balser
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Abstract

For a Euclidean building $X$ of type $A_{2}$, we classify the 0-dimensional subbuildings $A$ of $\partial_{T}X$ 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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BibTeXRIS

Andreas Balser. 2006-10-30. Convex rank 1 subsets of Euclidean buildings (of type $A_2$). https://arxiv.org/abs/math/0610947

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