2010/03/13 by Leonardo Biliotti, Biliotti, Leonardo, Alessandro Ghigi +1
Mathematics · #32M10 #53C35 #58J50 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Representation Theory (math.RT) #math.DG #math.RT #msc:32M10 #msc:53C35 #msc:58J50
paper · pdf · doi:10.48550/arxiv.1003.2725
A few misprints corrected. Reference added. To appear on American Journal of Mathematics
openalex publication_date 2010/03/13 · arxiv created 2010/12/09 · arxiv updated 2010/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a complex semisimple Lie group, K a maximal compact subgroup and V an irreducible representation of K. Denote by M the unique closed orbit of G in P(V) and by O its image via the moment map. For any measure on M we construct a map from the Satake compactification of G/K (associated to V) to the Lie algebra of K. For the K-invariant measure, this map is a homeomorphism of the Satake compactification onto the convex envelope of O. For a large class of measures the image of the map is the convex envelope. As an application we get sharp upper bounds for the first eigenvalue of the Laplacian on functions for an arbitrary Kaehler metric on a Hermitian symmetric space.