{"paper":{"title":"Local geodesics for plurisubharmonic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Alexander Rashkovskii","submitted_at":"2016-04-15T13:50:52Z","abstract_excerpt":"We study geodesics for plurisubharmonic functions from the Cegrell class ${\\mathcal F}_1$ on a bounded hyperconvex domain of ${\\mathbb C}^n$ and show that, as in the case of metrics on K\\\"{a}hler compact menifolds, they linearize an energy functional. As a consequence, we get a uniqueness theorem for functions from ${\\mathcal F}_1$ in terms of total masses of certain mixed Monge-Amp\\`ere currents. Geodesics of relative extremal functions are considered and a reverse Brunn-Minkowski inequality is proved for capacities of multiplicative combinations of multi-circled compact sets. We also show th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04504","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"}