Polygons with Prescribed Gauss Map in Hadamard Spaces and Euclidean Buildings
Printed: Sep 2006
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.
Moreover, the same result holds for
semistable configurations on arbitrary Euclidean buildings.
Euclidean buildings, Hadamard spaces, polygons
53C20 - Global Riemannian geometry, including pinching [See also 31C12, 58B20]