Prescribing scalar curvatures: loss of minimizability

Prescribing scalar curvatures: loss of minimizability

Prescribing conformally the scalar curvature on a closed manifold with negative Yamabe invariant as a given function \(K\) is possible under smallness assumptions on \(K_{+}=\max\{K,0\}\) and in particular, when \(K

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2024-07
Hauptverfasser: Mayer, Martin, Zhu, Chaona
Format: Artikel
Sprache:eng
Schlagworte:
Critical point
Curvature
Saddle points
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Mayer, Martin
Zhu, Chaona
description Prescribing conformally the scalar curvature on a closed manifold with negative Yamabe invariant as a given function \(K\) is possible under smallness assumptions on \(K_{+}=\max\{K,0\}\) and in particular, when \(K
format Article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_3069347997</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3069347997</sourcerecordid><originalsourceid>FETCH-proquest_journals_30693479973</originalsourceid><addsrcrecordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mQwDShKLU4uykzKzEtXKE5OzEksUkguLSpLLCkFSlgp5OQXFyvkpynkZuZl5mZWJSZl5mSWVPIwsKYl5hSn8kJpbgZlN9cQZw_dgqL8wtLU4pL4rPzSojygVLyxgZmlsYm5paW5MXGqAORvNck</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3069347997</pqid></control><display><type>article</type><title>Prescribing scalar curvatures: loss of minimizability</title><source>Freely Accessible Journals</source><creator>Mayer, Martin ; Zhu, Chaona</creator><creatorcontrib>Mayer, Martin ; Zhu, Chaona</creatorcontrib><description>Prescribing conformally the scalar curvature on a closed manifold with negative Yamabe invariant as a given function \(K\) is possible under smallness assumptions on \(K_{+}=\max\{K,0\}\) and in particular, when \(K&lt;0\). In addition, while solutions are unique in case \(K\leq 0\), non uniqueness generally holds, when \(K\) is sign changing and \(K_{+}\) sufficiently small and flat around its critical points. These solutions are found variationally as minimizers. Here we study, what happens, when the relevant arguments fail to apply, describing on one hand the loss of minimizability generally, while on the other we construct a function \(K\), for which saddle point solutions to the conformally prescribed scalar curvature problem still exist.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Critical point ; Curvature ; Saddle points</subject><ispartof>arXiv.org, 2024-07</ispartof><rights>2024. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</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>780,784</link.rule.ids></links><search><creatorcontrib>Mayer, Martin</creatorcontrib><creatorcontrib>Zhu, Chaona</creatorcontrib><title>Prescribing scalar curvatures: loss of minimizability</title><title>arXiv.org</title><description>Prescribing conformally the scalar curvature on a closed manifold with negative Yamabe invariant as a given function \(K\) is possible under smallness assumptions on \(K_{+}=\max\{K,0\}\) and in particular, when \(K&lt;0\). In addition, while solutions are unique in case \(K\leq 0\), non uniqueness generally holds, when \(K\) is sign changing and \(K_{+}\) sufficiently small and flat around its critical points. These solutions are found variationally as minimizers. Here we study, what happens, when the relevant arguments fail to apply, describing on one hand the loss of minimizability generally, while on the other we construct a function \(K\), for which saddle point solutions to the conformally prescribed scalar curvature problem still exist.</description><subject>Critical point</subject><subject>Curvature</subject><subject>Saddle points</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mQwDShKLU4uykzKzEtXKE5OzEksUkguLSpLLCkFSlgp5OQXFyvkpynkZuZl5mZWJSZl5mSWVPIwsKYl5hSn8kJpbgZlN9cQZw_dgqL8wtLU4pL4rPzSojygVLyxgZmlsYm5paW5MXGqAORvNck</recordid><startdate>20240703</startdate><enddate>20240703</enddate><creator>Mayer, Martin</creator><creator>Zhu, Chaona</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20240703</creationdate><title>Prescribing scalar curvatures: loss of minimizability</title><author>Mayer, Martin ; Zhu, Chaona</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_30693479973</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Critical point</topic><topic>Curvature</topic><topic>Saddle points</topic><toplevel>online_resources</toplevel><creatorcontrib>Mayer, Martin</creatorcontrib><creatorcontrib>Zhu, Chaona</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</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></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mayer, Martin</au><au>Zhu, Chaona</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Prescribing scalar curvatures: loss of minimizability</atitle><jtitle>arXiv.org</jtitle><date>2024-07-03</date><risdate>2024</risdate><eissn>2331-8422</eissn><abstract>Prescribing conformally the scalar curvature on a closed manifold with negative Yamabe invariant as a given function \(K\) is possible under smallness assumptions on \(K_{+}=\max\{K,0\}\) and in particular, when \(K&lt;0\). In addition, while solutions are unique in case \(K\leq 0\), non uniqueness generally holds, when \(K\) is sign changing and \(K_{+}\) sufficiently small and flat around its critical points. These solutions are found variationally as minimizers. Here we study, what happens, when the relevant arguments fail to apply, describing on one hand the loss of minimizability generally, while on the other we construct a function \(K\), for which saddle point solutions to the conformally prescribed scalar curvature problem still exist.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2024-07
issn 2331-8422
language eng
recordid cdi_proquest_journals_3069347997
source Freely Accessible Journals
subjects Critical point
Curvature
Saddle points
title Prescribing scalar curvatures: loss of minimizability
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-26T08%3A12%3A46IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Prescribing%20scalar%20curvatures:%20loss%20of%20minimizability&rft.jtitle=arXiv.org&rft.au=Mayer,%20Martin&rft.date=2024-07-03&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E3069347997%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=3069347997&rft_id=info:pmid/&rfr_iscdi=true