{"paper":{"title":"Homogenization of spectral problem on Riemannian manifold consisting of two domains connected by many tubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"Andrii Khrabustovskyi","submitted_at":"2010-11-17T10:35:42Z","abstract_excerpt":"The paper deals with the asymptotic behavior as $\\eps\\to 0$ of the spectrum of Laplace-Beltrami operator $\\Delta\\e$ on the Riemannian manifold $M\\e$ ($\\mathrm{\\dim} M\\e=N\\geq 2$) depending on a small parameter $\\eps>0$. $M\\e$ consists of two perforated domains which are connected by array of tubes of the length $q\\e$. Each perforated domain is obtained by removing from the fix domain $\\Omega\\subset \\mathbb{R}^N$ the system of $\\eps$-periodically distributed balls of the radius $d\\e=\\bar{o}(\\eps)$. We obtain a variety of homogenized spectral problems in $\\Omega$, their type depends on some rela"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3931","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":""},"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"}