{"paper":{"title":"Extremising eigenvalues of the GJMS operators in a fixed conformal class","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP","math.SP"],"primary_cat":"math.DG","authors_text":"Bruno Premoselli, Emmanuel Humbert, Romain Petrides","submitted_at":"2025-05-13T06:50:50Z","abstract_excerpt":"Let $(M,g)$ be a closed Riemannian manifold of dimension $n\\geq 3$. If $s$ is a positive integer satisfying $2s<n$, we let $P_g^s$ be the GJMS operator of order $2s$ in $M$. We investigate in this paper the extremal values taken by fixed eigenvalues of $P_h^s$ as $h$ runs through the whole conformal class $[g]$. These extremal values -- that we call throughout the paper \\emph{conformal eigenvalues} -- are conformal invariants of $(M,g)$ and optimisers for these problems, when they exist, are known to not be smooth metrics in general. In this paper we develop a general framework that allows us "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.08280","kind":"arxiv","version":2},"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/2505.08280/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"}