ON THE ASYMPTOTIC BEHAVIOR OF HOLOMORPHIC ISOMETRIES OF THE POINCARE DISK INTO BOUNDED SYMMETRIC DOMAINS-中国期刊网

摘要 InthisarticlewestudyholomorphicisometriesofthePoincar'ediskintoboundedsymmetricdomains.EarlierwesolvedtheproblemofanalyticcontinuationofgermsofholomorphicmapsbetweenboundeddomainswhichareisometriesuptonormalizingconstantswithrespecttotheBergmanmetric,showinginparticularthatthegraphV0ofanygermofholomorphicisometryofthePoincar'ediskΔintoanirreducibleboundedsymmetricdomainΩ€CNinitsHarish-Chandrarealizationmustextendtoanaffine-algebraicsubvarietyVC×CN=CN+1,andthattheirreduciblecomponentofV∩(Δ×Ω)containingV0isthegraphofaproperholomorphicisometricembeddingF:Δ→Ω.Inthisarticlewestudyholomorphicisometricembeddingswhichareasymptoticallygeodesicatageneralboundarypointb∈Δ.Startingwiththestructuralequationforholomor-phicisometriesarisingfromtheGaussequation,weobtainbycovariantdifferentiationanidentityrelatingcertainholomorphicbisectionalcurvaturestotheboundarybehaviorofthesecondfundamentalformσoftheholomorphicisometricembedding.Usingthenonpositivityofholomorphicbisectionalcurvaturesonaboundedsymmetricdomain,weprovethatσmustvanishatageneralboundarypointeithertotheorder1ortotheorder21,calledaholomorphicisometryofthefirstresp.secondkind.Wedealwithspecialcasesofnon-standardholomorphicisometricembeddingsofsuchmaps,showingthattheymustbeasymptoticallytotallygeodesicatageneralboundarypointandinfactofthefirstkindwheneverthetargetdomainisaCartesianproductofcomplexunitballs.WealsostudytheboundarybehaviorofanexampleofholomorphicisometricembeddingfromthePoincar'ediskintoaSiegelupperhalf-planebyanexplicitdeterminationoftheboundarybehaviorofholomorphicsectionalcurvaturesinthedirectionstangenttotheembeddedPoincar'edisk,showingthatthemapisindeedasymptoticallytotallygeodesicatageneralboundarypointandofthefirstkind.Fo

1GONGSHENG. THE BLOCH CONSTANT OF LOCALLY BIHOLOMORPHIC MAPPINGS ON BOUNDED SYMMETRIC DOMAINS.基础数学,1996-03.
2刘永民. SMALL HANKEL OPERATORS ON WEIGHTED BERGMAN SPACES OF BOUNDED SYMMETRIC DOMAINS.基础数学,2000-01.
3ZHANGWENJUN;RENFUYAO. RANDOM ITERAtION OF HOLOMORPHIC SELF-MAPS OVER BOUNDED DOMAINS IN C~N.基础数学,1995-01.
4Hideo KUBO;Koji KUBOTA. Existence and Asymptotic Behavior of Radially Symmetric Solutions to a Semilinear Hyperbolic System in Odd Space Dimensions.基础数学,2006-05.
5Yong Hua MAO. Lp-Poincare Inequality for General Symmetric Forms.基础数学,2009-12.
6Urs FRAUENFELDER;Otto van KOERT. Symmetric Periodic Orbits and Uniruled Real Liouville Domains.基础数学,2016-04.
7Oscar AGUDELO;Manuel DEL PINO;Juncheng WEI. Catenoidal Layers for the Allen-Cahn Equation in Bounded Domains.基础数学,2017-01.
8涂振汉;张莎莎. ON THE EXISTENCE OF SINGULAR DIRECTIONS OF HOLOMORPHIC MAPS FROM THE UNIT DISK INTO Pn（C）.基础数学,2010-05.
9Zhi Hua CHEN;Yang LIU. Schwarz-Pick Estimates for Bounded Holomorphic Functions in the Unit Ball of Cn.基础数学,2010-05.
10严加安;张土生. DIRICHLET FORMS AND SYMMETRIC DIFFUSIONS ON A BOUNDED DOMAIN IN R~d.基础数学,1990-04.

ON THE ASYMPTOTIC BEHAVIOR OF HOLOMORPHIC ISOMETRIES OF THE POINCARE DISK INTO BOUNDED SYMMETRIC DOMAINS

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ON THE ASYMPTOTIC BEHAVIOR OF HOLOMORPHIC ISOMETRIES OF THE POINCARE DISK INTO BOUNDED SYMMETRIC DOMAINS

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