An Isoperimetric Inequality for Planar Triangulations
We prove a discrete analogue to a classical isoperimetric theorem of Weil for surfaces with non-positive curvature. It is shown that hexagons in the triangular lattice have maximal volume among all sets of a given boundary in any triangulation with minimal degree 6.
Gespeichert in:
| Veröffentlicht in: | Discrete & computational geometry 2018-06, Vol.59 (4), p.802-809 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 809 |
|---|---|
| container_issue | 4 |
| container_start_page | 802 |
| container_title | Discrete & computational geometry |
| container_volume | 59 |
| creator | Angel, Omer Benjamini, Itai Horesh, Nizan |
| description | We prove a discrete analogue to a classical isoperimetric theorem of Weil for surfaces with non-positive curvature. It is shown that hexagons in the triangular lattice have maximal volume among all sets of a given boundary in any triangulation with minimal degree 6. |
| doi_str_mv | 10.1007/s00454-017-9942-3 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2038574902</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2038574902</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-6eced775e11046c1b671d48ec7892ea9f36069e28b099f67737f944e9d4943403</originalsourceid><addsrcrecordid>eNp1kD1PwzAQhi0EEqXwA9giMRvO9sWOx6rio1IlGMpsuemlShWc1k6G_nuMgsTEdMM973u6h7F7AY8CwDwlACyRgzDcWpRcXbCZQCU5IOIlm-WF5aUy-prdpHSAjFuoZqxchGKV-iPF9ouG2NbFKtBp9F07nIumj8VH54OPxSa2PuzHzg9tH9Itu2p8l-jud87Z58vzZvnG1--vq-VizWsl9MA11bQzpiQhAHUtttqIHVZUm8pK8rZRGrQlWW3B2kYbo0xjEcnu0KJCUHP2MPUeY38aKQ3u0I8x5JNOgqpKk5-QmRITVcc-pUiNO-ZvfDw7Ae7HjpvsuCzB_dhxKmfklEmZDXuKf83_h74BE5hl0Q</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2038574902</pqid></control><display><type>article</type><title>An Isoperimetric Inequality for Planar Triangulations</title><source>SpringerLink Journals</source><creator>Angel, Omer ; Benjamini, Itai ; Horesh, Nizan</creator><creatorcontrib>Angel, Omer ; Benjamini, Itai ; Horesh, Nizan</creatorcontrib><description>We prove a discrete analogue to a classical isoperimetric theorem of Weil for surfaces with non-positive curvature. It is shown that hexagons in the triangular lattice have maximal volume among all sets of a given boundary in any triangulation with minimal degree 6.</description><identifier>ISSN: 0179-5376</identifier><identifier>EISSN: 1432-0444</identifier><identifier>DOI: 10.1007/s00454-017-9942-3</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Combinatorics ; Computational Mathematics and Numerical Analysis ; Curvature ; Hexagons ; Mathematics ; Mathematics and Statistics ; Triangulation</subject><ispartof>Discrete & computational geometry, 2018-06, Vol.59 (4), p.802-809</ispartof><rights>Springer Science+Business Media, LLC 2017</rights><rights>Discrete & Computational Geometry is a copyright of Springer, (2017). All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-6eced775e11046c1b671d48ec7892ea9f36069e28b099f67737f944e9d4943403</citedby><cites>FETCH-LOGICAL-c316t-6eced775e11046c1b671d48ec7892ea9f36069e28b099f67737f944e9d4943403</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/s00454-017-9942-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00454-017-9942-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Angel, Omer</creatorcontrib><creatorcontrib>Benjamini, Itai</creatorcontrib><creatorcontrib>Horesh, Nizan</creatorcontrib><title>An Isoperimetric Inequality for Planar Triangulations</title><title>Discrete & computational geometry</title><addtitle>Discrete Comput Geom</addtitle><description>We prove a discrete analogue to a classical isoperimetric theorem of Weil for surfaces with non-positive curvature. It is shown that hexagons in the triangular lattice have maximal volume among all sets of a given boundary in any triangulation with minimal degree 6.</description><subject>Combinatorics</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Curvature</subject><subject>Hexagons</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Triangulation</subject><issn>0179-5376</issn><issn>1432-0444</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>BENPR</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1kD1PwzAQhi0EEqXwA9giMRvO9sWOx6rio1IlGMpsuemlShWc1k6G_nuMgsTEdMM973u6h7F7AY8CwDwlACyRgzDcWpRcXbCZQCU5IOIlm-WF5aUy-prdpHSAjFuoZqxchGKV-iPF9ouG2NbFKtBp9F07nIumj8VH54OPxSa2PuzHzg9tH9Itu2p8l-jud87Z58vzZvnG1--vq-VizWsl9MA11bQzpiQhAHUtttqIHVZUm8pK8rZRGrQlWW3B2kYbo0xjEcnu0KJCUHP2MPUeY38aKQ3u0I8x5JNOgqpKk5-QmRITVcc-pUiNO-ZvfDw7Ae7HjpvsuCzB_dhxKmfklEmZDXuKf83_h74BE5hl0Q</recordid><startdate>20180601</startdate><enddate>20180601</enddate><creator>Angel, Omer</creator><creator>Benjamini, Itai</creator><creator>Horesh, Nizan</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7XB</scope><scope>88I</scope><scope>8AL</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PADUT</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20180601</creationdate><title>An Isoperimetric Inequality for Planar Triangulations</title><author>Angel, Omer ; Benjamini, Itai ; Horesh, Nizan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-6eced775e11046c1b671d48ec7892ea9f36069e28b099f67737f944e9d4943403</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Combinatorics</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Curvature</topic><topic>Hexagons</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Triangulation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Angel, Omer</creatorcontrib><creatorcontrib>Benjamini, Itai</creatorcontrib><creatorcontrib>Horesh, Nizan</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</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>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>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</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>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>Research Library China</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>Discrete & computational geometry</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Angel, Omer</au><au>Benjamini, Itai</au><au>Horesh, Nizan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An Isoperimetric Inequality for Planar Triangulations</atitle><jtitle>Discrete & computational geometry</jtitle><stitle>Discrete Comput Geom</stitle><date>2018-06-01</date><risdate>2018</risdate><volume>59</volume><issue>4</issue><spage>802</spage><epage>809</epage><pages>802-809</pages><issn>0179-5376</issn><eissn>1432-0444</eissn><abstract>We prove a discrete analogue to a classical isoperimetric theorem of Weil for surfaces with non-positive curvature. It is shown that hexagons in the triangular lattice have maximal volume among all sets of a given boundary in any triangulation with minimal degree 6.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00454-017-9942-3</doi><tpages>8</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0179-5376 |
| ispartof | Discrete & computational geometry, 2018-06, Vol.59 (4), p.802-809 |
| issn | 0179-5376 1432-0444 |
| language | eng |
| recordid | cdi_proquest_journals_2038574902 |
| source | SpringerLink Journals |
| subjects | Combinatorics Computational Mathematics and Numerical Analysis Curvature Hexagons Mathematics Mathematics and Statistics Triangulation |
| title | An Isoperimetric Inequality for Planar Triangulations |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-30T08%3A01%3A23IST&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=An%20Isoperimetric%20Inequality%20for%20Planar%20Triangulations&rft.jtitle=Discrete%20&%20computational%20geometry&rft.au=Angel,%20Omer&rft.date=2018-06-01&rft.volume=59&rft.issue=4&rft.spage=802&rft.epage=809&rft.pages=802-809&rft.issn=0179-5376&rft.eissn=1432-0444&rft_id=info:doi/10.1007/s00454-017-9942-3&rft_dat=%3Cproquest_cross%3E2038574902%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=2038574902&rft_id=info:pmid/&rfr_iscdi=true |