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PureMathematicsnØêÆ,2023,13(4),1056-1061
PublishedOnlineApril2023inHans.https://www.hanspub.org/journal/pm
https://doi.org/10.12677/pm.2023.134111
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à¼ê§Green-OsherØª§Steinerõ‘ª
CurvatureIntegralInequalities
forSomeClassesofClosed
ConvexCurves
ZeyuanZhang
∗
,HuiwenZhao
SchoolofMathematics,YunnanNormalUniversity,KunmingYunnan
Received:Mar.20
th
,2023;accepted:Apr.21
st
,2023;published:Apr.28
th
,2023
∗ÏÕŠö"
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DOI:10.12677/pm.2023.134111
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Abstract
Green-Osherinequalityistheintegralofcurvatureforstrictlyconvexfunctionsin
general,somespecialconvexfunctionsgetcurvatureintegralinequalitiesinGreen-
Osherinequality.Inthispaper,weapplyfourtypesofconvexfunctionsofplane
closedconvexcurvetoGreen-Osherinequality.Wegetsomeexactlowerboundson
theintegrationoftheseconvexfunctionsoverthecurvature.Theselowerbounds
dependonlyonarclengthandarea.
Keywords
ConvexFunction,Green-OsherInequality,SteinerPolynomial
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.2023.1341111058nØêÆ
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DOI:10.12677/pm.2023.1341111059nØêÆ
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DOI:10.12677/pm.2023.1341111060nØêÆ
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[1]Green, M. andOsher, S.(1999)SteinerPolynomials, WulffFlows, andSome NewIsoperimetric
InequalitiesforConvexPlaneCurves.AsianJournalofMathematics,3,659-676.
https://doi.org/10.4310/AJM.1999.v3.n3.a5
[2]ê[,QSA.'u-ÇÈ©Øª5P[J].êÆ,“,2014,34(5):925-930.
https://doi.org/10.13548/j.sxzz.2014.05.040
[3]æx.Wulff6œ/e˜‡È©Øª[J].2ÀœhzóÆÆ,2015,25(1):67-68+73.
[4]æ ,ÂR,QSA,((.à-‚-ÇÈ©Øª[J/OL].êÆÆ(¥©‡):1-10.
http://kns.cnki.net/kcms/detail/11.2038.o1.20221108.1653.008.html
DOI:10.12677/pm.2023.1341111061nØêÆ

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