Rogers–Shephard and local Loomis–Whitney type inequalities

We provide functional analogues of the classical geometric inequality of Rogers and Shephard on products of volumes of sections and projections. As a consequence we recover (and obtain some new) functional versions of Rogers–Shephard type inequalities as well as some generalizations of the geometric...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematische annalen 2019-08, Vol.374 (3-4), p.1719-1771
Hauptverfasser: Alonso-Gutiérrez, David, Artstein-Avidan, Shiri, González Merino, Bernardo, Jiménez, Carlos Hugo, Villa, Rafael
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 1771
container_issue 3-4
container_start_page 1719
container_title Mathematische annalen
container_volume 374
creator Alonso-Gutiérrez, David
Artstein-Avidan, Shiri
González Merino, Bernardo
Jiménez, Carlos Hugo
Villa, Rafael
description We provide functional analogues of the classical geometric inequality of Rogers and Shephard on products of volumes of sections and projections. As a consequence we recover (and obtain some new) functional versions of Rogers–Shephard type inequalities as well as some generalizations of the geometric Rogers–Shephard inequality in the case where the subspaces intersect. These generalizations can be regarded as sharp local reverse Loomis–Whitney inequalities. We also obtain a sharp local Loomis–Whitney inequality.
doi_str_mv 10.1007/s00208-019-01834-3
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2264235836</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2264235836</sourcerecordid><originalsourceid>FETCH-LOGICAL-c363t-c194fd8c7380b9f2fa16804f0f82115952cfb942c511aaf463f3de3c081d38153</originalsourceid><addsrcrecordid>eNp9kM1Kw0AQxxdRsFZfwFPAc3RmJ5tuLoIUrUJB8AOPy3aza1PSJN1ND735Dr6hT-LWCN48DHP4fwzzY-wc4RIBJlcBgINMAYs4krKUDtgIM-IpSpgcslHURSok4TE7CWEFAAQgRuz6qX23Pnx9fD4vbbfUvkx0UyZ1a3SdzNt2Xe21t2XVN3aX9LvOJlVjN1tdV31lwyk7croO9ux3j9nr3e3L9D6dP84epjfz1FBOfWqwyFwpzYQkLArHncZcQubASY4oCsGNWxQZNwJRa5fl5Ki0ZEBiSRIFjdnF0Nv5drO1oVerduubeFJxnmec4mt5dPHBZXwbgrdOdb5aa79TCGrPSQ2cVOSkfjgpiiEaQiGamwjjr_qf1DfXQmvg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2264235836</pqid></control><display><type>article</type><title>Rogers–Shephard and local Loomis–Whitney type inequalities</title><source>Springer journals</source><creator>Alonso-Gutiérrez, David ; Artstein-Avidan, Shiri ; González Merino, Bernardo ; Jiménez, Carlos Hugo ; Villa, Rafael</creator><creatorcontrib>Alonso-Gutiérrez, David ; Artstein-Avidan, Shiri ; González Merino, Bernardo ; Jiménez, Carlos Hugo ; Villa, Rafael</creatorcontrib><description>We provide functional analogues of the classical geometric inequality of Rogers and Shephard on products of volumes of sections and projections. As a consequence we recover (and obtain some new) functional versions of Rogers–Shephard type inequalities as well as some generalizations of the geometric Rogers–Shephard inequality in the case where the subspaces intersect. These generalizations can be regarded as sharp local reverse Loomis–Whitney inequalities. We also obtain a sharp local Loomis–Whitney inequality.</description><identifier>ISSN: 0025-5831</identifier><identifier>EISSN: 1432-1807</identifier><identifier>DOI: 10.1007/s00208-019-01834-3</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Inequalities ; Inequality ; Mathematics ; Mathematics and Statistics ; Subspaces</subject><ispartof>Mathematische annalen, 2019-08, Vol.374 (3-4), p.1719-1771</ispartof><rights>Springer-Verlag GmbH Germany, part of Springer Nature 2019</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c363t-c194fd8c7380b9f2fa16804f0f82115952cfb942c511aaf463f3de3c081d38153</citedby><cites>FETCH-LOGICAL-c363t-c194fd8c7380b9f2fa16804f0f82115952cfb942c511aaf463f3de3c081d38153</cites><orcidid>0000-0002-5402-4150</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00208-019-01834-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00208-019-01834-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>315,782,786,27931,27932,41495,42564,51326</link.rule.ids></links><search><creatorcontrib>Alonso-Gutiérrez, David</creatorcontrib><creatorcontrib>Artstein-Avidan, Shiri</creatorcontrib><creatorcontrib>González Merino, Bernardo</creatorcontrib><creatorcontrib>Jiménez, Carlos Hugo</creatorcontrib><creatorcontrib>Villa, Rafael</creatorcontrib><title>Rogers–Shephard and local Loomis–Whitney type inequalities</title><title>Mathematische annalen</title><addtitle>Math. Ann</addtitle><description>We provide functional analogues of the classical geometric inequality of Rogers and Shephard on products of volumes of sections and projections. As a consequence we recover (and obtain some new) functional versions of Rogers–Shephard type inequalities as well as some generalizations of the geometric Rogers–Shephard inequality in the case where the subspaces intersect. These generalizations can be regarded as sharp local reverse Loomis–Whitney inequalities. We also obtain a sharp local Loomis–Whitney inequality.</description><subject>Inequalities</subject><subject>Inequality</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Subspaces</subject><issn>0025-5831</issn><issn>1432-1807</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9kM1Kw0AQxxdRsFZfwFPAc3RmJ5tuLoIUrUJB8AOPy3aza1PSJN1ND735Dr6hT-LWCN48DHP4fwzzY-wc4RIBJlcBgINMAYs4krKUDtgIM-IpSpgcslHURSok4TE7CWEFAAQgRuz6qX23Pnx9fD4vbbfUvkx0UyZ1a3SdzNt2Xe21t2XVN3aX9LvOJlVjN1tdV31lwyk7croO9ux3j9nr3e3L9D6dP84epjfz1FBOfWqwyFwpzYQkLArHncZcQubASY4oCsGNWxQZNwJRa5fl5Ki0ZEBiSRIFjdnF0Nv5drO1oVerduubeFJxnmec4mt5dPHBZXwbgrdOdb5aa79TCGrPSQ2cVOSkfjgpiiEaQiGamwjjr_qf1DfXQmvg</recordid><startdate>20190806</startdate><enddate>20190806</enddate><creator>Alonso-Gutiérrez, David</creator><creator>Artstein-Avidan, Shiri</creator><creator>González Merino, Bernardo</creator><creator>Jiménez, Carlos Hugo</creator><creator>Villa, Rafael</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-5402-4150</orcidid></search><sort><creationdate>20190806</creationdate><title>Rogers–Shephard and local Loomis–Whitney type inequalities</title><author>Alonso-Gutiérrez, David ; Artstein-Avidan, Shiri ; González Merino, Bernardo ; Jiménez, Carlos Hugo ; Villa, Rafael</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c363t-c194fd8c7380b9f2fa16804f0f82115952cfb942c511aaf463f3de3c081d38153</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Inequalities</topic><topic>Inequality</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Subspaces</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Alonso-Gutiérrez, David</creatorcontrib><creatorcontrib>Artstein-Avidan, Shiri</creatorcontrib><creatorcontrib>González Merino, Bernardo</creatorcontrib><creatorcontrib>Jiménez, Carlos Hugo</creatorcontrib><creatorcontrib>Villa, Rafael</creatorcontrib><collection>CrossRef</collection><jtitle>Mathematische annalen</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Alonso-Gutiérrez, David</au><au>Artstein-Avidan, Shiri</au><au>González Merino, Bernardo</au><au>Jiménez, Carlos Hugo</au><au>Villa, Rafael</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Rogers–Shephard and local Loomis–Whitney type inequalities</atitle><jtitle>Mathematische annalen</jtitle><stitle>Math. Ann</stitle><date>2019-08-06</date><risdate>2019</risdate><volume>374</volume><issue>3-4</issue><spage>1719</spage><epage>1771</epage><pages>1719-1771</pages><issn>0025-5831</issn><eissn>1432-1807</eissn><abstract>We provide functional analogues of the classical geometric inequality of Rogers and Shephard on products of volumes of sections and projections. As a consequence we recover (and obtain some new) functional versions of Rogers–Shephard type inequalities as well as some generalizations of the geometric Rogers–Shephard inequality in the case where the subspaces intersect. These generalizations can be regarded as sharp local reverse Loomis–Whitney inequalities. We also obtain a sharp local Loomis–Whitney inequality.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00208-019-01834-3</doi><tpages>53</tpages><orcidid>https://orcid.org/0000-0002-5402-4150</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0025-5831
ispartof Mathematische annalen, 2019-08, Vol.374 (3-4), p.1719-1771
issn 0025-5831
1432-1807
language eng
recordid cdi_proquest_journals_2264235836
source Springer journals
subjects Inequalities
Inequality
Mathematics
Mathematics and Statistics
Subspaces
title Rogers–Shephard and local Loomis–Whitney type inequalities
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-06T15%3A56%3A44IST&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=Rogers%E2%80%93Shephard%20and%20local%20Loomis%E2%80%93Whitney%20type%20inequalities&rft.jtitle=Mathematische%20annalen&rft.au=Alonso-Guti%C3%A9rrez,%20David&rft.date=2019-08-06&rft.volume=374&rft.issue=3-4&rft.spage=1719&rft.epage=1771&rft.pages=1719-1771&rft.issn=0025-5831&rft.eissn=1432-1807&rft_id=info:doi/10.1007/s00208-019-01834-3&rft_dat=%3Cproquest_cross%3E2264235836%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=2264235836&rft_id=info:pmid/&rfr_iscdi=true