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

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

2006-10-30

arxiv.org/abs/math/0610947v1

Mathematics

Metric Geometry

48 pages

Scientific paper

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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