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

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.

arXiv comment48 pages

References in corpus (1)

• Rigidity of invariant convex sets in symmetric spaces