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Convex functions on symmetric spaces, side lengths of polygons and stability inequalities for weighted configurations at infinity

Misha Kapovich·Bernhard Leeb·John J. Millson
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Abstract

In a symmetric space of noncompact type X = G/K oriented geodesic segments correspond to points in the Euclidean Weyl chamber. We can hence assign vector-valued side-lengths to segments. Our main result is a system of homogeneous linear inequalities describing the restrictions on the side -lengths of closed polygons. The inequalities are based on the mod 2 Schubert calculus in the real Grassmannians G/P for maximal parabolic subgroups P.

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Misha Kapovich, Bernhard Leeb, John J. Millson. 2005-11-06. Convex functions on symmetric spaces, side lengths of polygons and stability inequalities for weighted configurations at infinity. https://arxiv.org/abs/math/0311486

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