{"paper":{"title":"Stratifications with respect to actions of real reductive groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Gerald W. Schwarz, Henrik Stoetzel, Peter Heinzner","submitted_at":"2006-11-16T09:15:55Z","abstract_excerpt":"We study the action of a real reductive group G on a real submanifold X of a K\"ahler manifold Z. We suppose that the action of G extends holomorphically to an action of a complex reductive group and is Hamiltonian with respect to a compatible maximal compact subgroup of the complex reductive group. There is a corresponding gradient map obtained from a Cartan decomposition of G. We obtain a Morse like function on X. Associated to its critical points are various sets of semistable points which we study in great detail. In particular, we have G-stable submanifolds of X which are called pre-strata"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611491","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}