{"paper":{"title":"$\\Gamma$-convergence of the $p$-Dirichlet energy for manifold-valued maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giacomo Canevari, Giandomenico Orlandi, Ramon Oliver-Bonafoux, Van Phu Cuong Le","submitted_at":"2025-05-27T14:37:57Z","abstract_excerpt":"We prove a ${\\Gamma}$-convergence result for the $p$-Dirichlet energy functional defined on maps from a smooth bounded domain $\\Omega \\subseteq \\mathbb{R}^{n+k}$ to $\\mathscr{N}$, a $(k-2)$-connected and smooth closed Riemannian manifold with Abelian fundamental group, where $n$ and $k$ are integers, $n \\geq 0$, $k \\geq 2$. We focus on the regime $p \\to~k^-$ under Dirichlet boundary conditions. The result provides a description of the asymptotic behavior of the $\\textit{topological singular sets}$ for families of $\\mathscr{N}$-valued Sobolev maps which satisfy suitable energy bounds. Such topo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21257","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.21257/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}