Convex functions on symmetric spaces, side lengths of polygons and the stability inequalities for weighted configurations at infinity
By M. Kapovich, B. Leeb, John Millson. 2003
99 citations recorded by the source corpus.
In a symmetric space of noncompact type X = G=K oriented geodesic segments correspond modulo isometries to vectors in the Euclidean Weyl chamber. We can hence assign vector valued lengths to segments. Our main result is a system of homogeneous linear inequalities, which we call the generalized triangle inequalities or stability inequalities, describing the restrictions on the vector valued side lengths of oriented polygons. It is based on the mod 2 Schubert calculus in the real Grassmannians G=P for maximal parabolic subgroups P. The side lengths of polygons in Euclidean buildings are studied in the related paper [KLM2]. Applications of the geometric results in both papers to algebraic group theory are given in [KLM3].
Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/2abb4b0ab491b2313cc6f530a8d041a6aa68d051
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In Applied Mathematics
In Discrete Mathematics and Combinatorics
In Geometry and Topology
- Michael Kapovich
- J. Porti
- B. Leeb
- John Millson
- Anna Wienhard
- Arun Ram
- Christoph Schwer
- Jean-Marc Schlenker
Citations in the corpus
- The Generalized Triangle Inequalities in Symmetric Spaces and Buildings with Applications to Algebra (2002, methodology): “We note however that for these spaces, existence of a semistable configuration ψ on ∂T itsX implies existence of a nice semistable configuration on ∂T itsX, which has the same type as ψ, see [KLM1].”
- Anosov subgroups: dynamical and geometric characterizations (2017, background): “Similarly, one defines the -distance on euclidean buildings via apartment charts, see [17].”