{"paper":{"title":"Adiabatic compactness for holomorphic curves with boundary on nearby Lagrangians","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Daren Chen, Dylan Cant","submitted_at":"2023-02-26T19:17:50Z","abstract_excerpt":"In his 1989 paper, Floer established a connection between holomorphic strips with boundary on a Lagrangian $L$ and a small Hamiltonian push-off $L_{f}$, and gradient flow lines for the function $f$. The present paper studies the compactness theory for holomorphic curves $u_{n}$ whose boundary components lie on Hamiltonian perturbations $L_{n}^{1},\\dots,L^{N}_{n}$ of a fixed Lagrangian $L$, where each sequence of nearby Lagrangians $L^{j}_{n}$ converges to $L$ as $n\\to\\infty$. Generalizing earlier work of Oh, Fukaya, Ekholm, and Zhu, we prove that the limit of a sequence of such holomorphic map"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.13391","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/2302.13391/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"}