Eigenvalues under the Backward Ricci Flow on Locally Homogeneous Closed 3-manifolds
In this paper, we study the evolving behaviors of the first eigenvalue of the Laplace–Beltrami operator under the normalized backward Ricci flow, construct various quantities which are monotonic under the backward Ricci flow and get upper and lower bounds. We prove that in cases where the backward R...
Gespeichert in:
| Veröffentlicht in: | Acta mathematica Sinica. English series 2018-07, Vol.34 (7), p.1179-1194 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1194 |
|---|---|
| container_issue | 7 |
| container_start_page | 1179 |
| container_title | Acta mathematica Sinica. English series |
| container_volume | 34 |
| creator | Hou, Song Bo |
| description | In this paper, we study the evolving behaviors of the first eigenvalue of the Laplace–Beltrami operator under the normalized backward Ricci flow, construct various quantities which are monotonic under the backward Ricci flow and get upper and lower bounds. We prove that in cases where the backward Ricci flow converges to a sub-Riemannian geometry after a proper rescaling, the eigenvalue evolves toward zero. |
| doi_str_mv | 10.1007/s10114-018-6448-8 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_1993444621</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1993444621</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-a662798e34949a0de2c3e0b8ab31a760010058ba0eda6d31fbd91706451ed3563</originalsourceid><addsrcrecordid>eNp1kLtOwzAUhi0EEqXwAGyWmA0-sePYI1S9IFVC4jJbTuyUlDQudkPVt8dVOrAwnTP837l8CN0CvQdKi4cIFIATCpIIziWRZ2gEnClSCCjOT73MQVyiqxjXlOa5omKE3qbNynU_pu1dxH1nXcC7T4efTPW1N8Hi16aqGjxr_R77Di99Zdr2gBd-4xPmfB_xpPXRWczIxnRN7Vsbr9FFbdrobk51jD5m0_fJgixf5s-TxyWpGIgdMUJkhZKOccWVodZlFXO0lKZkYApBaXosl6WhzhphGdSlVVBQwXNwluWCjdHdMHcb_He6f6fXvg9dWqlBKcY5FxmkFAypKvgYg6v1NjQbEw4aqD6604M7ndzpozstE5MNTEzZbuXCn8n_Qr95wXBe</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1993444621</pqid></control><display><type>article</type><title>Eigenvalues under the Backward Ricci Flow on Locally Homogeneous Closed 3-manifolds</title><source>Alma/SFX Local Collection</source><source>SpringerLink Journals - AutoHoldings</source><creator>Hou, Song Bo</creator><creatorcontrib>Hou, Song Bo</creatorcontrib><description>In this paper, we study the evolving behaviors of the first eigenvalue of the Laplace–Beltrami operator under the normalized backward Ricci flow, construct various quantities which are monotonic under the backward Ricci flow and get upper and lower bounds. We prove that in cases where the backward Ricci flow converges to a sub-Riemannian geometry after a proper rescaling, the eigenvalue evolves toward zero.</description><identifier>ISSN: 1439-8516</identifier><identifier>EISSN: 1439-7617</identifier><identifier>DOI: 10.1007/s10114-018-6448-8</identifier><language>eng</language><publisher>Beijing: Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society</publisher><subject>Eigenvalues ; Lower bounds ; Mathematics ; Mathematics and Statistics ; Rescaling</subject><ispartof>Acta mathematica Sinica. English series, 2018-07, Vol.34 (7), p.1179-1194</ispartof><rights>Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018</rights><rights>Acta Mathematica Sinica, English Series is a copyright of Springer, (2018). All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-a662798e34949a0de2c3e0b8ab31a760010058ba0eda6d31fbd91706451ed3563</citedby><cites>FETCH-LOGICAL-c316t-a662798e34949a0de2c3e0b8ab31a760010058ba0eda6d31fbd91706451ed3563</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/s10114-018-6448-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10114-018-6448-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27906,27907,41470,42539,51301</link.rule.ids></links><search><creatorcontrib>Hou, Song Bo</creatorcontrib><title>Eigenvalues under the Backward Ricci Flow on Locally Homogeneous Closed 3-manifolds</title><title>Acta mathematica Sinica. English series</title><addtitle>Acta. Math. Sin.-English Ser</addtitle><description>In this paper, we study the evolving behaviors of the first eigenvalue of the Laplace–Beltrami operator under the normalized backward Ricci flow, construct various quantities which are monotonic under the backward Ricci flow and get upper and lower bounds. We prove that in cases where the backward Ricci flow converges to a sub-Riemannian geometry after a proper rescaling, the eigenvalue evolves toward zero.</description><subject>Eigenvalues</subject><subject>Lower bounds</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Rescaling</subject><issn>1439-8516</issn><issn>1439-7617</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1kLtOwzAUhi0EEqXwAGyWmA0-sePYI1S9IFVC4jJbTuyUlDQudkPVt8dVOrAwnTP837l8CN0CvQdKi4cIFIATCpIIziWRZ2gEnClSCCjOT73MQVyiqxjXlOa5omKE3qbNynU_pu1dxH1nXcC7T4efTPW1N8Hi16aqGjxr_R77Di99Zdr2gBd-4xPmfB_xpPXRWczIxnRN7Vsbr9FFbdrobk51jD5m0_fJgixf5s-TxyWpGIgdMUJkhZKOccWVodZlFXO0lKZkYApBaXosl6WhzhphGdSlVVBQwXNwluWCjdHdMHcb_He6f6fXvg9dWqlBKcY5FxmkFAypKvgYg6v1NjQbEw4aqD6604M7ndzpozstE5MNTEzZbuXCn8n_Qr95wXBe</recordid><startdate>20180701</startdate><enddate>20180701</enddate><creator>Hou, Song Bo</creator><general>Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KR7</scope><scope>L.-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M0N</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20180701</creationdate><title>Eigenvalues under the Backward Ricci Flow on Locally Homogeneous Closed 3-manifolds</title><author>Hou, Song Bo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-a662798e34949a0de2c3e0b8ab31a760010058ba0eda6d31fbd91706451ed3563</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Eigenvalues</topic><topic>Lower bounds</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Rescaling</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hou, Song Bo</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ABI/INFORM Global</collection><collection>Computing Database</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>One Business (ProQuest)</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Acta mathematica Sinica. English series</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hou, Song Bo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Eigenvalues under the Backward Ricci Flow on Locally Homogeneous Closed 3-manifolds</atitle><jtitle>Acta mathematica Sinica. English series</jtitle><stitle>Acta. Math. Sin.-English Ser</stitle><date>2018-07-01</date><risdate>2018</risdate><volume>34</volume><issue>7</issue><spage>1179</spage><epage>1194</epage><pages>1179-1194</pages><issn>1439-8516</issn><eissn>1439-7617</eissn><abstract>In this paper, we study the evolving behaviors of the first eigenvalue of the Laplace–Beltrami operator under the normalized backward Ricci flow, construct various quantities which are monotonic under the backward Ricci flow and get upper and lower bounds. We prove that in cases where the backward Ricci flow converges to a sub-Riemannian geometry after a proper rescaling, the eigenvalue evolves toward zero.</abstract><cop>Beijing</cop><pub>Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society</pub><doi>10.1007/s10114-018-6448-8</doi><tpages>16</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1439-8516 |
| ispartof | Acta mathematica Sinica. English series, 2018-07, Vol.34 (7), p.1179-1194 |
| issn | 1439-8516 1439-7617 |
| language | eng |
| recordid | cdi_proquest_journals_1993444621 |
| source | Alma/SFX Local Collection; SpringerLink Journals - AutoHoldings |
| subjects | Eigenvalues Lower bounds Mathematics Mathematics and Statistics Rescaling |
| title | Eigenvalues under the Backward Ricci Flow on Locally Homogeneous Closed 3-manifolds |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-17T11%3A10%3A29IST&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=Eigenvalues%20under%20the%20Backward%20Ricci%20Flow%20on%20Locally%20Homogeneous%20Closed%203-manifolds&rft.jtitle=Acta%20mathematica%20Sinica.%20English%20series&rft.au=Hou,%20Song%20Bo&rft.date=2018-07-01&rft.volume=34&rft.issue=7&rft.spage=1179&rft.epage=1194&rft.pages=1179-1194&rft.issn=1439-8516&rft.eissn=1439-7617&rft_id=info:doi/10.1007/s10114-018-6448-8&rft_dat=%3Cproquest_cross%3E1993444621%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=1993444621&rft_id=info:pmid/&rfr_iscdi=true |