{"paper":{"title":"Strong submultiplicativity of the Poincare metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Daniela Kraus, Oliver Roth","submitted_at":"2016-03-22T15:07:01Z","abstract_excerpt":"We give a direct proof of an important result of Solynin which says that the Poincar\\'e metric is a strongly submultiplicative domain function. This result is then used to define a new capacity for compact subsets of the complex plane $\\mathbb{C}$, which might be called Poincar\\'e capacity. If the compact set $K \\subseteq \\mathbb{C}$ is connected, then the Poincar\\'e capacity of $K$ is the same as the logarithmic capacity of $K$. In this special case, the submultiplicativity is well--known and can be stated as an inequality for the normalized conformal map onto the complement of $K$. Using the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06818","kind":"arxiv","version":1},"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"}