The spectrum of the Laplacian on forms over flat manifolds

In this article we prove that the spectrum of the Laplacian on k -forms over a non compact flat manifold is always a connected closed interval of the non negative real line. The proof is based on a detailed decomposition of the structure of flat manifolds.

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Mathematische Zeitschrift 2020-10, Vol.296 (1-2), p.1-12
Hauptverfasser:	Charalambous, Nelia, Lu, Zhiqin
Format:	Artikel
Sprache:	eng
Schlagworte:	Manifolds Mathematics Mathematics and Statistics
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

container_end_page	12
container_issue	1-2
container_start_page	1
container_title	Mathematische Zeitschrift
container_volume	296
creator	Charalambous, Nelia Lu, Zhiqin
description	In this article we prove that the spectrum of the Laplacian on k -forms over a non compact flat manifold is always a connected closed interval of the non negative real line. The proof is based on a detailed decomposition of the structure of flat manifolds.
doi_str_mv	10.1007/s00209-019-02407-5
format	Article
fullrecord	<record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2437414436</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2437414436</sourcerecordid><originalsourceid>FETCH-LOGICAL-c270t-1e7b43b591955b9ab52889c9a8ba5deed36f36540adf0b8b75db754509edb69e3</originalsourceid><addsrcrecordid>eNp9UMtKxDAUDaLgOPoDrgKuozevpnEngy8YcDOuQ9ImOkPb1KQj-PdmrODOxeFyOY_LPQhdUrimAOomAzDQBGgBE6CIPEILKjgjtGb8GC0KL4mslThFZznvAAqpxALdbt49zqNvprTvcQx4Kvvajp1ttnbAccAhpj7j-OkTDp2dcG-HbYhdm8_RSbBd9he_c4leH-43qyeyfnl8Xt2tScMUTIR65QR3UlMtpdPWSVbXutG2dla23re8CrySAmwbwNVOybZASNC-dZX2fImu5twxxY-9z5PZxX0ayknDDk9QIXhVVGxWNSnmnHwwY9r2Nn0ZCubQkZk7MqUj89ORkcXEZ1Mu4uHNp7_of1zffc9oow</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2437414436</pqid></control><display><type>article</type><title>The spectrum of the Laplacian on forms over flat manifolds</title><source>Springer Nature - Complete Springer Journals</source><creator>Charalambous, Nelia ; Lu, Zhiqin</creator><creatorcontrib>Charalambous, Nelia ; Lu, Zhiqin</creatorcontrib><description>In this article we prove that the spectrum of the Laplacian on k -forms over a non compact flat manifold is always a connected closed interval of the non negative real line. The proof is based on a detailed decomposition of the structure of flat manifolds.</description><identifier>ISSN: 0025-5874</identifier><identifier>EISSN: 1432-1823</identifier><identifier>DOI: 10.1007/s00209-019-02407-5</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Manifolds ; Mathematics ; Mathematics and Statistics</subject><ispartof>Mathematische Zeitschrift, 2020-10, Vol.296 (1-2), p.1-12</ispartof><rights>Springer-Verlag GmbH Germany, part of Springer Nature 2019</rights><rights>Springer-Verlag GmbH Germany, part of Springer Nature 2019.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-1e7b43b591955b9ab52889c9a8ba5deed36f36540adf0b8b75db754509edb69e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00209-019-02407-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00209-019-02407-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Charalambous, Nelia</creatorcontrib><creatorcontrib>Lu, Zhiqin</creatorcontrib><title>The spectrum of the Laplacian on forms over flat manifolds</title><title>Mathematische Zeitschrift</title><addtitle>Math. Z</addtitle><description>In this article we prove that the spectrum of the Laplacian on k -forms over a non compact flat manifold is always a connected closed interval of the non negative real line. The proof is based on a detailed decomposition of the structure of flat manifolds.</description><subject>Manifolds</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0025-5874</issn><issn>1432-1823</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9UMtKxDAUDaLgOPoDrgKuozevpnEngy8YcDOuQ9ImOkPb1KQj-PdmrODOxeFyOY_LPQhdUrimAOomAzDQBGgBE6CIPEILKjgjtGb8GC0KL4mslThFZznvAAqpxALdbt49zqNvprTvcQx4Kvvajp1ttnbAccAhpj7j-OkTDp2dcG-HbYhdm8_RSbBd9he_c4leH-43qyeyfnl8Xt2tScMUTIR65QR3UlMtpdPWSVbXutG2dla23re8CrySAmwbwNVOybZASNC-dZX2fImu5twxxY-9z5PZxX0ayknDDk9QIXhVVGxWNSnmnHwwY9r2Nn0ZCubQkZk7MqUj89ORkcXEZ1Mu4uHNp7_of1zffc9oow</recordid><startdate>20201001</startdate><enddate>20201001</enddate><creator>Charalambous, Nelia</creator><creator>Lu, Zhiqin</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20201001</creationdate><title>The spectrum of the Laplacian on forms over flat manifolds</title><author>Charalambous, Nelia ; Lu, Zhiqin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-1e7b43b591955b9ab52889c9a8ba5deed36f36540adf0b8b75db754509edb69e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Manifolds</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Charalambous, Nelia</creatorcontrib><creatorcontrib>Lu, Zhiqin</creatorcontrib><collection>CrossRef</collection><jtitle>Mathematische Zeitschrift</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Charalambous, Nelia</au><au>Lu, Zhiqin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The spectrum of the Laplacian on forms over flat manifolds</atitle><jtitle>Mathematische Zeitschrift</jtitle><stitle>Math. Z</stitle><date>2020-10-01</date><risdate>2020</risdate><volume>296</volume><issue>1-2</issue><spage>1</spage><epage>12</epage><pages>1-12</pages><issn>0025-5874</issn><eissn>1432-1823</eissn><abstract>In this article we prove that the spectrum of the Laplacian on k -forms over a non compact flat manifold is always a connected closed interval of the non negative real line. The proof is based on a detailed decomposition of the structure of flat manifolds.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00209-019-02407-5</doi><tpages>12</tpages></addata></record>
fulltext	fulltext
identifier	ISSN: 0025-5874
ispartof	Mathematische Zeitschrift, 2020-10, Vol.296 (1-2), p.1-12
issn	0025-5874 1432-1823
language	eng
recordid	cdi_proquest_journals_2437414436
source	Springer Nature - Complete Springer Journals
subjects	Manifolds Mathematics Mathematics and Statistics
title	The spectrum of the Laplacian on forms over flat manifolds
url	https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-25T03%3A00%3A48IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20spectrum%20of%20the%20Laplacian%20on%20forms%20over%20flat%20manifolds&rft.jtitle=Mathematische%20Zeitschrift&rft.au=Charalambous,%20Nelia&rft.date=2020-10-01&rft.volume=296&rft.issue=1-2&rft.spage=1&rft.epage=12&rft.pages=1-12&rft.issn=0025-5874&rft.eissn=1432-1823&rft_id=info:doi/10.1007/s00209-019-02407-5&rft_dat=%3Cproquest_cross%3E2437414436%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2437414436&rft_id=info:pmid/&rfr_iscdi=true