arXiv math/03114862003-11math.DGmath.AG

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

Misha Kapovich, Bernhard Leeb, John J. Millson

英文摘要：

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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