La lecture à portée de main
Découvre YouScribe en t'inscrivant gratuitement
Je m'inscrisDécouvre YouScribe en t'inscrivant gratuitement
Je m'inscrisDescription
Sujets
Informations
Publié par | pefav |
Nombre de lectures | 18 |
Langue | English |
Extrait
theLoiscalseFcurvatouthistheoremcorre-andsectionthewisedensitbytangenofrecenenergygivongeometricmanifoldsfunctionsof31C35,negativ|eanifoldscurv(seeatureferencesarisedydiscretFAnotherrtheaedsectiontegralericheMoutonsAbstractcLetoutialboundednesse|anegativharmonicoffunctionreferonhistoricalaudcompleteergence.simplyofconnectedasmanifoldwMofwhosendsectionalthecurvtheaturesJ.areosebanoundedebfettialwineKey-wentttegralwwnianotionnegativteoincoofnvsttialannitenessts.tialItRiemannianispincprocurvvtheedwnianhereWareaderpforoinandtthewiseofcriterionconofynon-atangenhtialOneconexistencevanaloguesergencesolvfother(seepasoingeometrictsondingofonetheygeomeintricbb(seeounthedary:thisthegivnitenesser.of,thethatdensitterpretationyareaoftheenergy.,wwhicducehyis:theFgeoemareaenegativtric|analogueyofssicthe:densit60J45.ywofpthetareacriteriainnon-tangentegralconinergencethenon-tangenEubcandlideanofhalf-space.non-tangenInenergytroonductionmIfofthehedstudyeofaturenon-tangenytialusecBroomotionn[16]).veergencetheoftohaarticlerthemdetailsonicrefunctionsonbsteganyinnon-1906tialwithvtheManwquestionsell-knoaswnconsequencetheoremtofeFresults.atouw(seethe[11]),ofietandbeecameedcleartlyincasethetrees1970s[17]).(seewfortoexamplea[14])criterionthatspspacestoofEuclideannegativonedensitcurvofatureareaprotegralvideenaynat-Brossardural[6])\geometric"ndsettingpurpforofthisarticlestudy:toasecananswbIne1seenwinrecallsecthetioinno1,thesevin-eralisnotionsnon-tangenhaenergyvIne4,simplereortromoretnaturaldensitexpressionsinordsthisharmonicgeometric|setting.atouFypromtheoremthis|pinoin|teofatureview,Browmotion.eMath.prolavaed2000some31C12,y58J65,ears1ago.ofcurvenergy(aseratoraorgeometrictroinwnterpretation(softhethequidensitycurvofconstanthedareayinernels,tegral.areAgain,nthisusgeometricaexpressionalsoisthesimplerethansimplytheetE2udieo-cDenotelideanassoone.enInMor-bderbtowithproxvwseatthatthenotionniteness,ofkthis)densite).ywillimpliesinalmostpincevberywhereanifoldthearenon-tangenwtialconhasvCartanergenceopwdetherstbreAscallandandloMartincalyFbatodesicudenotetheorem@due@toandHitoshiesAraiwhic(seeeither[4])motioninthesection[19]).3.ilyA2newmeasuresproneoftofPoissonthatlimitresultoispalsoxgivoentbWywreningtheseargumenmotsettingsnegativusedLetinaaRiemannianprevioussec-wtorkounded(seeeen[16]).negativAbstraightforw0.ardeencorollaryHadamardofMthistoloballcaldFMaytBeltramioMuGtGreenheoremwnis.T.aScp[3])oinA.t[1]),wiseoundaryone:denednon-tangGreeneitsn,tialthebys,oundednessefromuniqbbelo.wmeasuresiswhenalmomonicstwnianevmeerywherexequivMalenctetoexitnon-tangenBrotialatconyvhletergencye.eWae=then)proofvalenethenthemain.reosul2tde