{"corpus_id":10366083,"paper_sha":"fe735ec79f70186878353d6ad653dd077d5aa657","doi":"10.1098/rspa.2004.1356","arxiv_id":"math-ph/0405039","pmid":null,"pmcid":null,"mag_id":2097554753,"dblp_id":null,"acl_id":null,"title":"A lower bound to the spectral threshold in curved tubes","year":2004,"publication_date":"2004-05-13","venue":"Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences","journal":{"name":"Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences","pages":"3457 - 3467","volume":"460"},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics","Physics"],"reference_count":21,"citation_count":26,"influential_citation_count":0,"is_open_access":true,"arxiv_categories":["math-ph","cond-mat.mes-hall","math.MP","math.SP","quant-ph"],"arxiv_license":null,"arxiv_journal_ref":"R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 460 (2004), no.\n  2052, 3457-3467","mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":"https://arxiv.org/pdf/math-ph/0405039","s2_open_access_landing_url":"https://www.semanticscholar.org/paper/fe735ec79f70186878353d6ad653dd077d5aa657","s2_open_access_license":null,"s2_open_access_status":"GREEN","pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"We consider the Laplacian in curved tubes of arbitrary cross–section rotating together with the Frenet frame along curves in Euclidean spaces of arbitrary dimension, subject to Dirichlet boundary conditions on the cylindrical surface and Neumann conditions at the ends of the tube. 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