{"paper":{"title":"Extremal functions for modules of systems of measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexander Vasil'ev, Irina Markina, Melkana Brakalova","submitted_at":"2014-09-04T22:26:48Z","abstract_excerpt":"We study Fuglede's $p$-module of systems of measures in condensers in Euclidean spaces and on polarizable Carnot groups. We apply and generalize a result by Rodin, which provides an explicit method for finding the extremal function and the 2-module of a foliated family of curves in $\\mathbb R^2$, to a variety of settings. In the planar case, we apply Rodin's method to obtain estimates for the conformal module of a parallelogram and of a ring domain using directional dilatations. In $\\mathbb R^n,$ we identify the extremal function and compute the $p$-module of images of families of connecting c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1626","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"}