Convex functions on symmetric spaces and geometric invariant theory for weighted configurations on flag manifolds
نویسندگان
چکیده
3 Convex functions on symmetric spaces 11 3.1 Geometric preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.1.1 Metric spaces with curvature bounds . . . . . . . . . . . . . . 11 3.1.2 Hadamard spaces . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1.3 Symmetric spaces of noncompact type . . . . . . . . . . . . . 15 3.1.4 Auxiliary results . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 Measures on the ideal boundary of symmetric spaces . . . . . . . . . 20 3.2.1 Definition of stability . . . . . . . . . . . . . . . . . . . . . . . 21 3.2.2 Stable measures . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2.3 Unstable measures and directions of steepest descent . . . . . 23 3.2.4 Nice semistable measures: The structure of minimum sets . . 25 3.2.5 Asymptotically semistable measures and folding . . . . . . . . 27
منابع مشابه
Convex functions on symmetric spaces and geometric invariant theory for spaces of weighted configurations on flag manifolds
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