资源描述：
《alexandov space with curvature bounded below》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、HomeSearchCollectionsJournalsAboutContactusMyIOPscienceA.D.AlexandrovspaceswithcurvatureboundedbelowThisarticlehasbeendownloadedfromIOPscience.Pleasescrolldowntoseethefulltextarticle.1992Russ.Math.Surv.471(http://iopscience.iop.org/0036-0279/47/2/R01)Viewthetableofcontentsfort
2、hisissue,orgotothejournalhomepageformoreDownloaddetails:IPAddress:193.51.104.69Thearticlewasdownloadedon27/09/2010at16:27Pleasenotethattermsandconditionsapply.UspekhiMatNauk47:2(1992),3-51RussianMath.Surveys47:2(1992),1-58A.D.Alexandrovspaceswithcurvatureboundedbelow(1)Yu.Bura
3、go,M.Gromov,andG.Perel'manCONTENTS§1.Introduction1§2.Basicconcepts4§3.Globalizationtheorem7§4.Naturalconstructions13§5.Burstpoints16§6.Dimension20§7.Thetangentconeandthespaceofdirections.Conventionsandnotation22§8.Estimatesofroughvolumeandthecompactnesstheorem31§9.Theoremonalm
4、ostisometry33§10.Hausdorffmeasure40§11.Functionsthathavedirectionalderivatives,themethodofsuccessive43approximations,levelsurfacesofalmostregularmaps§12.Levellinesofalmostregularmaps49§13.Subsequentresultsandopenquestions53References56§1.Introduction1.1.Inthispaperwedevelopthe
5、theoryof(basicallyfinite-dimensional)metricspaceswithcurvature(inthesenseofAlexandrov)boundedbelow[1],[2].Wearetalking,roughlyspeaking,aboutspaceswithanintrinsicmetric,forwhichtheconclusionofToponogov'sanglecomparisontheoremistrue(althoughonlyinthesmall);forprecisedefinitionss
6、ee§2.Thesespacesaredefinedaxiomaticallybytheirlocalgeometricproperties,withoutthetechniquesofanalysis.Theymayhavemetricandtopologicalsingularities,inparticular,theymaynotbemanifolds.TheclassconsideredincludesalllimitspacesofsequencesofcompleteRiemannianmanifoldswithsectionalcu
7、rvatureuniformlyboundedbelow.AlexandrovspacesarisenaturallyifRiemannianmanifoldsareconsideredfromtheviewpointofsyntheticgeometryandoneavoidstheexcessiveassumptionsofsmoothnessconnectedmWehaveusedthisspellingofAlexandrov,ratherthanAleksandrov,becauseofthetitleofthepaper(inEngli
8、sh)mentionedonp.4.(Ed.)2Yu.Burago,Μ.Gromov,andG.Perel'manwith
