{"paper":{"title":"Geodesics in the space of K\\\"ahler cone metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Kai Zheng, Simone Calamai","submitted_at":"2012-04-30T23:49:21Z","abstract_excerpt":"In this paper, we study the Dirichlet problem of the geodesic equation in the space of K\\\"ahler cone metrics $\\mathcal H_\\b$; that is equivalent to a homogeneous complex Monge-Amp\\`ere equation whose boundary values consist of K\\\"ahler metrics with cone singularities. Our approach concerns the generalization of the space defined in Donaldson \\cite{MR2975584} to the case of K\\\"ahler manifolds with boundary; moreover we introduce a subspace $\\mathcal H_C$ of $\\mathcal H_\\b$ which we define by prescribing appropriate geometric conditions. Our main result is the existence, uniqueness and regularit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0056","kind":"arxiv","version":4},"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"}