Delaunay decompositions minimizing energy of weighted toroidal graphs

Delaunay decompositions minimizing energy of weighted toroidal graphs

Given a weighted toroidal graph, each realization to a Euclidean torus is associated with the Dirichlet energy. By minimizing the energy over all possible Euclidean structures and over all realizations within a fixed homotopy class, one obtains a harmonic map into an optimal Euclidean torus. We show...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
1. Verfasser: Lam, Wai Yeung
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Differential Geometry
Mathematics - Mathematical Physics
Mathematics - Metric Geometry
Physics - Mathematical Physics
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 Lam, Wai Yeung
description Given a weighted toroidal graph, each realization to a Euclidean torus is associated with the Dirichlet energy. By minimizing the energy over all possible Euclidean structures and over all realizations within a fixed homotopy class, one obtains a harmonic map into an optimal Euclidean torus. We show that only with this optimal Euclidean structure, the harmonic map and the edge weights are induced from a weighted Delaunay decomposition.
doi_str_mv 10.48550/arxiv.2203.03846
format Article
fullrecord <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2203_03846</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2203_03846</sourcerecordid><originalsourceid>FETCH-LOGICAL-a676-df246f6b00cd6683a991357104f1c5cc9e0a76e6959e2cb77defa37c71d62cc03</originalsourceid><addsrcrecordid>eNotz7tOwzAUgGEvDKjwAEz4BRJ8ie14RKVcpEpduken9nFqKbEjJ1zC0yMK07_90kfIHWd10yrFHqB8xY9aCCZrJttGX5PdEw7wnmClHl0epzzHJeY00zGmOMbvmHqKCUu_0hzoJ8b-vKCnSy45ehhoX2A6zzfkKsAw4-1_N-T4vDtuX6v94eVt-7ivQBtd-SAaHfSJMee1biVYy6UynDWBO-WcRQZGo7bKonAnYzwGkMYZ7rVwjskNuf_bXhzdVOIIZe1-Pd3FI38AZ3hG0w</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Delaunay decompositions minimizing energy of weighted toroidal graphs</title><source>arXiv.org</source><creator>Lam, Wai Yeung</creator><creatorcontrib>Lam, Wai Yeung</creatorcontrib><description>Given a weighted toroidal graph, each realization to a Euclidean torus is associated with the Dirichlet energy. By minimizing the energy over all possible Euclidean structures and over all realizations within a fixed homotopy class, one obtains a harmonic map into an optimal Euclidean torus. We show that only with this optimal Euclidean structure, the harmonic map and the edge weights are induced from a weighted Delaunay decomposition.</description><identifier>DOI: 10.48550/arxiv.2203.03846</identifier><language>eng</language><subject>Mathematics - Differential Geometry ; Mathematics - Mathematical Physics ; Mathematics - Metric Geometry ; Physics - Mathematical Physics</subject><creationdate>2022-03</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>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2203.03846$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2203.03846$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Lam, Wai Yeung</creatorcontrib><title>Delaunay decompositions minimizing energy of weighted toroidal graphs</title><description>Given a weighted toroidal graph, each realization to a Euclidean torus is associated with the Dirichlet energy. By minimizing the energy over all possible Euclidean structures and over all realizations within a fixed homotopy class, one obtains a harmonic map into an optimal Euclidean torus. We show that only with this optimal Euclidean structure, the harmonic map and the edge weights are induced from a weighted Delaunay decomposition.</description><subject>Mathematics - Differential Geometry</subject><subject>Mathematics - Mathematical Physics</subject><subject>Mathematics - Metric Geometry</subject><subject>Physics - Mathematical Physics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz7tOwzAUgGEvDKjwAEz4BRJ8ie14RKVcpEpduken9nFqKbEjJ1zC0yMK07_90kfIHWd10yrFHqB8xY9aCCZrJttGX5PdEw7wnmClHl0epzzHJeY00zGmOMbvmHqKCUu_0hzoJ8b-vKCnSy45ehhoX2A6zzfkKsAw4-1_N-T4vDtuX6v94eVt-7ivQBtd-SAaHfSJMee1biVYy6UynDWBO-WcRQZGo7bKonAnYzwGkMYZ7rVwjskNuf_bXhzdVOIIZe1-Pd3FI38AZ3hG0w</recordid><startdate>20220307</startdate><enddate>20220307</enddate><creator>Lam, Wai Yeung</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220307</creationdate><title>Delaunay decompositions minimizing energy of weighted toroidal graphs</title><author>Lam, Wai Yeung</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a676-df246f6b00cd6683a991357104f1c5cc9e0a76e6959e2cb77defa37c71d62cc03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics - Differential Geometry</topic><topic>Mathematics - Mathematical Physics</topic><topic>Mathematics - Metric Geometry</topic><topic>Physics - Mathematical Physics</topic><toplevel>online_resources</toplevel><creatorcontrib>Lam, Wai Yeung</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Lam, Wai Yeung</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Delaunay decompositions minimizing energy of weighted toroidal graphs</atitle><date>2022-03-07</date><risdate>2022</risdate><abstract>Given a weighted toroidal graph, each realization to a Euclidean torus is associated with the Dirichlet energy. By minimizing the energy over all possible Euclidean structures and over all realizations within a fixed homotopy class, one obtains a harmonic map into an optimal Euclidean torus. We show that only with this optimal Euclidean structure, the harmonic map and the edge weights are induced from a weighted Delaunay decomposition.</abstract><doi>10.48550/arxiv.2203.03846</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext_linktorsrc
identifier DOI: 10.48550/arxiv.2203.03846
ispartof
issn
language eng
recordid cdi_arxiv_primary_2203_03846
source arXiv.org
subjects Mathematics - Differential Geometry
Mathematics - Mathematical Physics
Mathematics - Metric Geometry
Physics - Mathematical Physics
title Delaunay decompositions minimizing energy of weighted toroidal graphs
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-28T23%3A34%3A48IST&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=Delaunay%20decompositions%20minimizing%20energy%20of%20weighted%20toroidal%20graphs&rft.au=Lam,%20Wai%20Yeung&rft.date=2022-03-07&rft_id=info:doi/10.48550/arxiv.2203.03846&rft_dat=%3Carxiv_GOX%3E2203_03846%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