{"paper":{"title":"Continuity of nonlinear eigenvalues in $CD(K,\\infty)$ spaces with respect to measured Gromov-Hausdorff convergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.SP"],"primary_cat":"math.MG","authors_text":"Jacobus W. Portegies, Luigi Ambrosio, Shouhei Honda","submitted_at":"2017-06-26T13:37:26Z","abstract_excerpt":"In this note we prove in the nonlinear setting of $CD(K,\\infty)$ spaces the stability of the Krasnoselskii spectrum of the Laplace operator $-\\Delta$ under measured Gromov-Hausdorff convergence, under an additional compactness assumption satisfied, for instance, by sequences of $CD^*(K,N)$ metric measure spaces with uniformly bounded diameter. Additionally, we show that every element $\\lambda$ in the Krasnoselskii spectrum is indeed an eigenvalue, namely there exists a nontrivial $u$ satisfying the eigenvalue equation $- \\Delta u = \\lambda u$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08368","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":""},"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"}