{"paper":{"title":"Convexity theorems for the gradient map on probability measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alberto Raffero, Leonardo Biliotti","submitted_at":"2017-01-17T17:34:53Z","abstract_excerpt":"Given a K\\\"ahler manifold $(Z,J,\\omega)$ and a compact real submanifold $M\\subset Z$, we study the properties of the gradient map associated with the action of a noncompact real reductive Lie group ${\\rm G}$ on the space of probability measures on $M.$ In particular, we prove convexity results for such map when ${\\rm G}$ is Abelian and we investigate how to extend them to the non-Abelian case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04779","kind":"arxiv","version":3},"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"}