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PureMathematicsnØêÆ,2023,13(3),375-380
PublishedOnlineMarch2023inHans.https://www.hanspub.org/journal/pm
https://doi.org/10.12677/pm.2023.133041
{ü4à-‚-ÇÈ©Øª
4í'X
oooææ惃ƒ
∗
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Á‡
©Ì‡ïIJ¡þ{ü4à-‚-ÇÈ©Øª"|^ü „Ç{•6éGreen-Osher
(J?1{zy²§uy-ÇÈ©Øª pÚ$œ¹˜‡4í'X§é±c(J?
1í2§¿…uy˜‡AÏ¼ê"
'…c
ü „Ç{•6§-ÇÈ©Øª§{ü4à-‚
RecurrenceRelationofCurvature
IntegralInequalitiesforSimple
ClosedConvexCurves
YazunLi
∗
,YongzhiZhang
YunnanNormalUniversity,KunmingYunnan
Received:Jan.24
th
,2023;accepted:Feb.23
rd
,2023;published:Mar.2
nd
,2023
∗ÏÕŠö"
©ÙÚ^:oæƒ,Ü[“.{ü4à-‚-ÇÈ©Øª4í'X[J].nØêÆ,2023,13(3):375-380.
DOI:10.12677/pm.2023.133041
o惧Ü[“
Abstract
Inthispaper, wemainlystudythecurvatureintegralinequalityofsimpleclosedconvex
curves ontheplane.We usetheunit-speedoutwardnormalflow tosimplifytheproof
ofGreen-Osher’sresults,findarecurrencerelationshipbetweenthehigh-orderand
low-ordercasesofthecurvatureintegralinequality,generalizethepreviousresults,
andfindaspecialfunction.
Keywords
TheUnit-SpeedOutwardNormalFlow,TheCurvatureIntegralInequality,Simple
ClosedConvexCurves
Copyright
c
2023byauthor(s)andHansPublishersInc.
This work is licensed undertheCreative Commons Attribution International License (CCBY 4.0).
http://creativecommons.org/licenses/by/4.0/
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DOI:10.12677/pm.2023.133041376nØêÆ
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DOI:10.12677/pm.2023.133041377nØêÆ
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DOI:10.12677/pm.2023.133041378nØêÆ
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DOI:10.12677/pm.2023.133041379nØêÆ
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ë•©z
[1]Gage,M.E.(1983)AnIsoperimetricInequalitywithApplicationtoShortening.DukeMathe-
maticalJournal,50,1225-1229.https://doi.org/10.1215/S0012-7094-83-05052-4
[2]ê[,QSA.'u-ÇÈ©Øª5P[J].êÆ,“,2014,34(5):925-930.
[3]Gao,L.Y.,Pan,S.L.andTsai,D.-H.(2021)OnanArea-PreservingInverseCurvatureFlow
ofConvexClosedPlaneCurve.JournalofFunctionalAnalysis,280,ArticleID:108931.
https://doi.org/10.1016/j.jfa.2021.108931
[4]),/Æ,Œ.Gage±Øª\r/ª[J].êÆcr,2008,29A(3):301-306.
[5]Green,M.andOsher,S.(1999)SteinerPolnomials,WulffFlow,andSomeNewIsoperimetric
InequalitiesforConvexPlaneCurves.TheAsianJournalofMathematics,3,659-676.
https://doi.org/10.4310/AJM.1999.v3.n3.a5
DOI:10.12677/pm.2023.133041380nØêÆ

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