{"paper":{"title":"An isoperimetric inequality for eigenvalues of the bi-harmonic operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"G. Feng, Q. Ding, Y. Zhang","submitted_at":"2011-01-27T08:56:06Z","abstract_excerpt":"} In this article, we put forward a Neumann eigenvalue problem for the bi-harmonic operator $\\Delta^2$ on a bounded smooth domain $\\Om$ in the Euclidean $n$-space ${\\bf R}^n$ ($n\\ge2$) and then prove that the corresponding first non-zero eigenvalue $\\Upsilon_1(\\Om)$ admits the isoperimetric inequality of Szeg\\\"o-Weinberger type: $\\Upsilon_1(\\Om)\\le \\Upsilon_1(B_{\\Om})$, where $B_{\\Om}$ is a ball in ${\\bf R}^n$ with the same volume of $\\Om$. The isoperimetric inequality of Szeg\\\"o-Weinberger type for the first nonzero Neumann eigenvalue of the even-multi-Laplacian operators $\\Delta^{2m}$ ($m\\ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5224","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"}