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.

Keywords:

Euclidean buildings, Hadamard spaces, polygons Euclidean buildings, Hadamard spaces, polygons

MSC Classifications:

53C20 show english descriptions Global Riemannian geometry, including pinching [See also 31C12, 58B20] 53C20 - Global Riemannian geometry, including pinching [See also 31C12, 58B20]

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