{"paper":{"title":"Asymptotic analysis for approximate harmonic maps from degenerating cylinders and applications to minimal surfaces","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jiayu Li, Lei Liu, Miaomiao Zhu","submitted_at":"2026-05-20T14:01:58Z","abstract_excerpt":"We investigate the blow-up analysis and quantitative behavior for a sequence of maps $\\{u_n\\}_{n=1}^\\infty$ from degenerating tori $(T^2,g_n)$ or from degenerating cylinders $(S^1\\times [0,\\pi],g_n)$ with free boundary conditions $u_n(S^1\\times \\{0,\\pi\\})\\subset K$ to a compact Riemannian manifold $(N,h)$ satisfying $$E(u_n)+\\|\\tau(u_n,g_n)\\|_{L^2}\\leq \\Lambda<\\infty,$$ where $\\tau(u_n,g_n)$ is the tension field of $u_n$, $K\\subset N$ is a smooth submanifold. We establish generalized energy identities and prove that away from bubbles, the asymptotic limit of the necks are either some geodesics"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21202","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/2605.21202/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"}