{"paper":{"title":"Variational approximation of size-mass energies for k-dimensional currents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonin Chambolle (CMAP), Beno\\^it Merlet (LPP, Luca Alberto Davide Ferrari (CMAP), RAPSODI)","submitted_at":"2017-10-24T14:42:56Z","abstract_excerpt":"In this paper we produce a $$\\Gamma$$-convergence result for a class of energies $F k $\\epsilon$,a$ modeled on the Ambrosio-Tortorelli functional. For the choice k = 1 we show that $F 1 $\\epsilon$,a $\\Gamma$$-converges to a branched transportation energy whose cost per unit length is a function $f n--1 a$ depending on a parameter $a > 0$ and on the codimension n -- 1. The limit cost f a (m) is bounded from below by 1 + m so that the limit functional controls the mass and the length of the limit object. In the limit a $\\downarrow$ 0 we recover the Steiner energy. We then generalize the approach"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08808","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"}