A short proof of Hadwiger's characterization theorem

A short proof of Hadwiger's characterization theorem

One of the most beautiful and important results in geometric convexity is Hadwiger's characterization theorem for the quermassintegrals. Hadwiger's theorem classifies all continuous rigid motion invariant valuations on convex bodies as consisting of the linear span of the quermassintegrals...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematika 1995-12, Vol.42 (2), p.329-339
1. Verfasser: Klain, Daniel A.
Format: Artikel
Sprache:eng
Schlagworte:
52A39
52A39: CONVEX AND DISCRETE GEOMETRY
CONVEX AND DISCRETE GEOMETRY
General Convexity
Mixed volumes and related topics
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 339
container_issue 2
container_start_page 329
container_title Mathematika
container_volume 42
creator Klain, Daniel A.
description One of the most beautiful and important results in geometric convexity is Hadwiger's characterization theorem for the quermassintegrals. Hadwiger's theorem classifies all continuous rigid motion invariant valuations on convex bodies as consisting of the linear span of the quermassintegrals (or, equivalently, of the intrinsic volumes) [4]. Hadwiger's characterization leads to effortless proofs of numerous results in integral geometry, including various kinematic formulas [7, 9] and the mean projection formulas for convex bodies [10]. Hadwiger's result also provides a connection between rigid motion invariant set functions and symmetric polynomials [1, 7].
doi_str_mv 10.1112/S0025579300014625
format Article
fullrecord <record><control><sourceid>cambridge_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1112_S0025579300014625</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cupid>10_1112_S0025579300014625</cupid><sourcerecordid>10_1112_S0025579300014625</sourcerecordid><originalsourceid>FETCH-LOGICAL-c4535-11294f860043dc1cec436c1e5e044a1af56219f0b136d3698e7d8c8c18ae94e23</originalsourceid><addsrcrecordid>eNqFkE9PAjEQxRujiYh-AG9787Ta6b_dPSJRMGKMAY23pnRnoQiUtGsQP71LIF40mkwyhzfvl_eGkHOglwDAroaUMimzglNKQSgmD0iLUQFpVgh2SFpbOd3qx-QkxhmlUuUCWkR0kjj1oU5WwfsqaaZvyrWbYLiIiZ2aYGyNwX2a2vllUk_RB1yckqPKzCOe7XebPN_ejLr9dPDYu-t2BqkVksu0yVWIKleUCl5asGgFVxZQIhXCgKmkYlBUdAxclVwVOWZlbnMLucFCIONtAjuuDT7GgJVeBbcwYaOB6m1t_aN24-nuPGs3x83_Bv0wuv-Nku4oLtb48U0x4U2rjGdSq96T7r3wazkUoF-be75Pahbj4MoJ6pl_D8vmO39k_QL_ynla</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>A short proof of Hadwiger's characterization theorem</title><source>Wiley Online Library All Journals</source><creator>Klain, Daniel A.</creator><creatorcontrib>Klain, Daniel A.</creatorcontrib><description>One of the most beautiful and important results in geometric convexity is Hadwiger's characterization theorem for the quermassintegrals. Hadwiger's theorem classifies all continuous rigid motion invariant valuations on convex bodies as consisting of the linear span of the quermassintegrals (or, equivalently, of the intrinsic volumes) [4]. Hadwiger's characterization leads to effortless proofs of numerous results in integral geometry, including various kinematic formulas [7, 9] and the mean projection formulas for convex bodies [10]. Hadwiger's result also provides a connection between rigid motion invariant set functions and symmetric polynomials [1, 7].</description><identifier>ISSN: 0025-5793</identifier><identifier>EISSN: 2041-7942</identifier><identifier>DOI: 10.1112/S0025579300014625</identifier><language>eng</language><publisher>London, UK: London Mathematical Society</publisher><subject>52A39 ; 52A39: CONVEX AND DISCRETE GEOMETRY ; CONVEX AND DISCRETE GEOMETRY ; General Convexity ; Mixed volumes and related topics</subject><ispartof>Mathematika, 1995-12, Vol.42 (2), p.329-339</ispartof><rights>Copyright © University College London 1995</rights><rights>1995 University College London</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c4535-11294f860043dc1cec436c1e5e044a1af56219f0b136d3698e7d8c8c18ae94e23</citedby><cites>FETCH-LOGICAL-c4535-11294f860043dc1cec436c1e5e044a1af56219f0b136d3698e7d8c8c18ae94e23</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1112%2FS0025579300014625$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1112%2FS0025579300014625$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Klain, Daniel A.</creatorcontrib><title>A short proof of Hadwiger's characterization theorem</title><title>Mathematika</title><addtitle>Mathematika</addtitle><description>One of the most beautiful and important results in geometric convexity is Hadwiger's characterization theorem for the quermassintegrals. Hadwiger's theorem classifies all continuous rigid motion invariant valuations on convex bodies as consisting of the linear span of the quermassintegrals (or, equivalently, of the intrinsic volumes) [4]. Hadwiger's characterization leads to effortless proofs of numerous results in integral geometry, including various kinematic formulas [7, 9] and the mean projection formulas for convex bodies [10]. Hadwiger's result also provides a connection between rigid motion invariant set functions and symmetric polynomials [1, 7].</description><subject>52A39</subject><subject>52A39: CONVEX AND DISCRETE GEOMETRY</subject><subject>CONVEX AND DISCRETE GEOMETRY</subject><subject>General Convexity</subject><subject>Mixed volumes and related topics</subject><issn>0025-5793</issn><issn>2041-7942</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1995</creationdate><recordtype>article</recordtype><recordid>eNqFkE9PAjEQxRujiYh-AG9787Ta6b_dPSJRMGKMAY23pnRnoQiUtGsQP71LIF40mkwyhzfvl_eGkHOglwDAroaUMimzglNKQSgmD0iLUQFpVgh2SFpbOd3qx-QkxhmlUuUCWkR0kjj1oU5WwfsqaaZvyrWbYLiIiZ2aYGyNwX2a2vllUk_RB1yckqPKzCOe7XebPN_ejLr9dPDYu-t2BqkVksu0yVWIKleUCl5asGgFVxZQIhXCgKmkYlBUdAxclVwVOWZlbnMLucFCIONtAjuuDT7GgJVeBbcwYaOB6m1t_aN24-nuPGs3x83_Bv0wuv-Nku4oLtb48U0x4U2rjGdSq96T7r3wazkUoF-be75Pahbj4MoJ6pl_D8vmO39k_QL_ynla</recordid><startdate>199512</startdate><enddate>199512</enddate><creator>Klain, Daniel A.</creator><general>London Mathematical Society</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>199512</creationdate><title>A short proof of Hadwiger's characterization theorem</title><author>Klain, Daniel A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c4535-11294f860043dc1cec436c1e5e044a1af56219f0b136d3698e7d8c8c18ae94e23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1995</creationdate><topic>52A39</topic><topic>52A39: CONVEX AND DISCRETE GEOMETRY</topic><topic>CONVEX AND DISCRETE GEOMETRY</topic><topic>General Convexity</topic><topic>Mixed volumes and related topics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Klain, Daniel A.</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><jtitle>Mathematika</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Klain, Daniel A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A short proof of Hadwiger's characterization theorem</atitle><jtitle>Mathematika</jtitle><addtitle>Mathematika</addtitle><date>1995-12</date><risdate>1995</risdate><volume>42</volume><issue>2</issue><spage>329</spage><epage>339</epage><pages>329-339</pages><issn>0025-5793</issn><eissn>2041-7942</eissn><abstract>One of the most beautiful and important results in geometric convexity is Hadwiger's characterization theorem for the quermassintegrals. Hadwiger's theorem classifies all continuous rigid motion invariant valuations on convex bodies as consisting of the linear span of the quermassintegrals (or, equivalently, of the intrinsic volumes) [4]. Hadwiger's characterization leads to effortless proofs of numerous results in integral geometry, including various kinematic formulas [7, 9] and the mean projection formulas for convex bodies [10]. Hadwiger's result also provides a connection between rigid motion invariant set functions and symmetric polynomials [1, 7].</abstract><cop>London, UK</cop><pub>London Mathematical Society</pub><doi>10.1112/S0025579300014625</doi><tpages>11</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0025-5793
ispartof Mathematika, 1995-12, Vol.42 (2), p.329-339
issn 0025-5793
2041-7942
language eng
recordid cdi_crossref_primary_10_1112_S0025579300014625
source Wiley Online Library All Journals
subjects 52A39
52A39: CONVEX AND DISCRETE GEOMETRY
CONVEX AND DISCRETE GEOMETRY
General Convexity
Mixed volumes and related topics
title A short proof of Hadwiger's characterization theorem
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-08T03%3A25%3A49IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-cambridge_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20short%20proof%20of%20Hadwiger's%20characterization%20theorem&rft.jtitle=Mathematika&rft.au=Klain,%20Daniel%20A.&rft.date=1995-12&rft.volume=42&rft.issue=2&rft.spage=329&rft.epage=339&rft.pages=329-339&rft.issn=0025-5793&rft.eissn=2041-7942&rft_id=info:doi/10.1112/S0025579300014625&rft_dat=%3Ccambridge_cross%3E10_1112_S0025579300014625%3C/cambridge_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_cupid=10_1112_S0025579300014625&rfr_iscdi=true