[
    {
        "id": "authors:5k26m-b1s32",
        "collection": "authors",
        "collection_id": "5k26m-b1s32",
        "cite_using_url": "https://authors.library.caltech.edu/records/5k26m-b1s32",
        "type": "article",
        "title": "Adiabatic compactness for holomorphic curves with boundary on nearby Lagrangians",
        "author": [
            {
                "family_name": "Cant",
                "given_name": "Dylan",
                "orcid": "0000-0002-6894-0504"
            },
            {
                "family_name": "Chen",
                "given_name": "Daren",
                "orcid": "0000-0002-5637-447X",
                "clpid": "Chen-Daren"
            }
        ],
        "abstract": "<p>In a 1989 paper [14], Floer established a connection between holomorphic strips with boundary on a Lagrangian L and a small Hamiltonian push-off Lf and gradient flow lines for the function f. The present paper studies the compactness theory for holomorphic curves un whose boundary components lie on Hamiltonian perturbations Ln1,&hellip;,LnN of a fixed Lagrangian L, where each sequence of nearby Lagrangians Lnj converges to L as n&rarr;&infin;. Generalizing earlier work of Oh, Fukaya, Ekholm, and Zhu, we prove that the limit of a sequence of such holomorphic maps is a configuration consisting of holomorphic curves with boundary on L joined by gradient flow lines connecting points on the boundary of holomorphic pieces. The key new result is an exponential estimate analyzing the interface between the holomorphic parts and the gradient flow line parts.</p>",
        "doi": "10.1215/21562261-2024-0043",
        "issn": "2156-2261",
        "publisher": "Duke University Press",
        "publication": "Kyoto Journal of Mathematics",
        "publication_date": "2026-05",
        "series_number": "2",
        "volume": "66",
        "issue": "2"
    }
]