Sharp $L^2$ estimates for the drift heat equation on shrinking Ricci solitons
We prove an $L^2$ estimate for the drift heat equation on a complete gradient shrinking Ricci soliton. This estimate has a time-dependent weight which is Gaussian in its spatial asymptotics. When transferred and scaled to an estimate for the heat equation along the Ricci flow of the soliton, this es...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | |
| container_volume | |
| creator | Macbeth, Heather |
| description | We prove an $L^2$ estimate for the drift heat equation on a complete gradient
shrinking Ricci soliton. This estimate has a time-dependent weight which is
Gaussian in its spatial asymptotics. When transferred and scaled to an estimate
for the heat equation along the Ricci flow of the soliton, this estimate is
uniform up to the singular time. |
| doi_str_mv | 10.48550/arxiv.2402.03304 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2402_03304</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2402_03304</sourcerecordid><originalsourceid>FETCH-LOGICAL-a674-13de31724514c3716333c96abe8756094c153aa2d074b084c1fb8449d1c453723</originalsourceid><addsrcrecordid>eNotj7FOwzAURb0woMIHMPGGrgm233OcjFVFASkICToTOY5DrJaktQ2CvycUpCtd3eXoHsauBM-pVIrfmPDlP3NJXOYckdM5e3wZTDjAsn6VS3Ax-XeTXIR-CpAGB13wfYLBmQTu-GGSn0aYE4fgx50f3-DZW-shTnufpjFesLPe7KO7_O8F225ut-v7rH66e1iv6swUmjKBnUOhJSlBFrUoENFWhWldqVXBK7JCoTGy45paXs6zb0uiqhOWFGqJC3b9hz35NIcwvw7fza9Xc_LCH0jMRmQ</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Sharp $L^2$ estimates for the drift heat equation on shrinking Ricci solitons</title><source>arXiv.org</source><creator>Macbeth, Heather</creator><creatorcontrib>Macbeth, Heather</creatorcontrib><description>We prove an $L^2$ estimate for the drift heat equation on a complete gradient
shrinking Ricci soliton. This estimate has a time-dependent weight which is
Gaussian in its spatial asymptotics. When transferred and scaled to an estimate
for the heat equation along the Ricci flow of the soliton, this estimate is
uniform up to the singular time.</description><identifier>DOI: 10.48550/arxiv.2402.03304</identifier><language>eng</language><subject>Mathematics - Differential Geometry</subject><creationdate>2024-02</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2402.03304$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2402.03304$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Macbeth, Heather</creatorcontrib><title>Sharp $L^2$ estimates for the drift heat equation on shrinking Ricci solitons</title><description>We prove an $L^2$ estimate for the drift heat equation on a complete gradient
shrinking Ricci soliton. This estimate has a time-dependent weight which is
Gaussian in its spatial asymptotics. When transferred and scaled to an estimate
for the heat equation along the Ricci flow of the soliton, this estimate is
uniform up to the singular time.</description><subject>Mathematics - Differential Geometry</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj7FOwzAURb0woMIHMPGGrgm233OcjFVFASkICToTOY5DrJaktQ2CvycUpCtd3eXoHsauBM-pVIrfmPDlP3NJXOYckdM5e3wZTDjAsn6VS3Ax-XeTXIR-CpAGB13wfYLBmQTu-GGSn0aYE4fgx50f3-DZW-shTnufpjFesLPe7KO7_O8F225ut-v7rH66e1iv6swUmjKBnUOhJSlBFrUoENFWhWldqVXBK7JCoTGy45paXs6zb0uiqhOWFGqJC3b9hz35NIcwvw7fza9Xc_LCH0jMRmQ</recordid><startdate>20240205</startdate><enddate>20240205</enddate><creator>Macbeth, Heather</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20240205</creationdate><title>Sharp $L^2$ estimates for the drift heat equation on shrinking Ricci solitons</title><author>Macbeth, Heather</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a674-13de31724514c3716333c96abe8756094c153aa2d074b084c1fb8449d1c453723</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics - Differential Geometry</topic><toplevel>online_resources</toplevel><creatorcontrib>Macbeth, Heather</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Macbeth, Heather</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Sharp $L^2$ estimates for the drift heat equation on shrinking Ricci solitons</atitle><date>2024-02-05</date><risdate>2024</risdate><abstract>We prove an $L^2$ estimate for the drift heat equation on a complete gradient
shrinking Ricci soliton. This estimate has a time-dependent weight which is
Gaussian in its spatial asymptotics. When transferred and scaled to an estimate
for the heat equation along the Ricci flow of the soliton, this estimate is
uniform up to the singular time.</abstract><doi>10.48550/arxiv.2402.03304</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | DOI: 10.48550/arxiv.2402.03304 |
| ispartof | |
| issn | |
| language | eng |
| recordid | cdi_arxiv_primary_2402_03304 |
| source | arXiv.org |
| subjects | Mathematics - Differential Geometry |
| title | Sharp $L^2$ estimates for the drift heat equation on shrinking Ricci solitons |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-22T08%3A05%3A38IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Sharp%20$L%5E2$%20estimates%20for%20the%20drift%20heat%20equation%20on%20shrinking%20Ricci%20solitons&rft.au=Macbeth,%20Heather&rft.date=2024-02-05&rft_id=info:doi/10.48550/arxiv.2402.03304&rft_dat=%3Carxiv_GOX%3E2402_03304%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |