{"paper":{"title":"Energy local minimizers for the nonlinear Schr\\\"{o}dinger equation on product spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dario Pierotti, Gianmaria Verzini, Junwei Yu","submitted_at":"2025-06-27T16:37:04Z","abstract_excerpt":"We investigate the existence of local minimizers with prescribed $L^2$-norm for the energy functional associated to the mass-supercritical nonlinear Schr\\\"{o}dinger equation on the product space $\\mathbb{R}^N \\times M^k$, where $(M^k,g)$ is a compact Riemannian manifold, thus complementing the study of the mass-subcritical case performed by Terracini, Tzvetkov and Visciglia in [\\emph{Anal. PDE} 2014, arXiv:1205.0342].\n  First we prove that, for small $L^2$-mass, the problem admits local minimizers. Next, we show that when the $L^2$-norm is sufficiently small, the local minimizers are constants"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.22371","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/2506.22371/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"}