arXiv subjects
Publications and source records attributed to Andreas Balser.
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.
We show that given a stable weighted configuration on the asymptotic boundary of a locally compact Hadamard space, there is a polygon with Gauss map prescribed by the given weighted configuration if the configuration is stable. Moreover, the same result holds for semistable configurations on arbitrary Euclidean buildings. We also examine how rays project to closed convex subsets of Hadamard spaces.
We study convex subsets of buildings, discuss some structural features and derive several characterizations of buildings.
We prove that two dimensional convex subsets of spherical buildings are either buildings or have a center.
We derive necessary conditions on the parameters of the ends of a CMC-1 trinoid in hyperbolic 3-space $H^{3}$ with symmetry plane by passing to its conjugate minimal surface. Together with Daniel's results, this yields a classification of generic symmetric trinoids. We also discuss the relation to other classification results of trinoids by Bobenko et al. and Umehara-Yamada. To obtain the result above, we show that the conjugate minimal surface of a catenoidal CMC-1 end in $H^{3}$ with symmetry plane is asymptotic to a suitable helicoid.