{"paper":{"title":"Condensers with infinitely many touching Borel plates and minimum energy problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Natalia Zorii","submitted_at":"2019-03-21T10:47:32Z","abstract_excerpt":"Defining a condenser in a locally compact space as a locally finite, countable collection of Borel sets $A_i$, $i\\in I$, with the sign $s_i=\\pm1$ prescribed such that $A_i\\cap A_j=\\varnothing$ whenever $s_is_j=-1$, we consider a minimum energy problem with an external field over infinite dimensional vector measures $(\\mu^i)_{i\\in I}$, where $\\mu^i$ is a suitably normalized positive Radon measure carried by $A_i$ and such that $\\mu^i\\leqslant\\xi^i$ for all $i\\in I_0$, $I_0\\subset I$ and constraints $\\xi^i$, $i\\in I_0$, being given. If $I_0=\\varnothing$, the problem reduces to the (unconstrained"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08917","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"}