黎曼曲面

图书标准信息

• 作者 H.M.Farkas 著
• 出版社 世界图书出版公司
• 出版时间 2003-09
• 版次 2
• ISBN 9787506259477
• 定价 34.00元
• 装帧 平装
• 开本 其他
• 纸张 胶版纸
• 页数 363页

【内容简介】

Itisgratifyingtolearnthatthereisnewlifeinanoldfieldthathasbeenatthecenterofonesexistenceforoveraquarterofacentury.ItisparticularlypleasingthatthesubjectofRiemannsurfaceshasattractedtheattentionofanewgenerationofmathematiciansfrom（newly）adjacentfields（forexample，thoseinterestedinhyperbolicmanifoldsanditerationsofrationalmaps）andyoungphysicistswhohavebeenconvinced（certainlynotbymathematicians）thatcompactRiemannsurfacesmayplayanimportantroleintheir（string）universe.Wehopethatnon-mathematiciansaswellasmathematicians（workinginnearbyareastothecentraltopicofthisbook）willalsolearnpartofthissubjectforthesheerbeautyandeleganceofthematerial（workofWeierstrass，Jacobi，Riemann，Hilbert，Weyl）andashealthyexposuretotheway（some）mathematicianswriteaboutmathematics.

【目录】

PrefacetotheSecondEdition
PrefacetotheFirstEdition
CommonlyUsedSymbols
CHAPTER0AnOverview
0.1.TopologicalAspects，Uniformization，andFuchsianGroups
0.2.AlgebraicFunctions
0.3.AbelianVarieties
0.4.MoreAnalyticAspects

CHAPTERⅠRiemannSurfaces
Ⅰ.1.DefinitionsandExamples
Ⅰ.2.TopologyofRiemannSurfaces
Ⅰ.3.DifferentialForms
Ⅰ.4.IntegrationFormulae

CHAPTERⅡExistenceTheorems
Ⅱ.1.HilbertSpaceTheory--AQuickReview
Ⅱ.2.Weyl‘sLemma
Ⅱ.3.TheHilbertSpaceofSquarelntegrableForms
Ⅱ.4.HarmonicDifferentials
Ⅱ.5.MeromorphicFunctionsandDifferentials
CHAPTERⅢCompactRiemannSurfaces
CHAPTERⅣUniformization
CHAPTERⅤAutomorphismsofCompactSurfaces-ElementaryTheory
CHAPTERⅥThetaFunctions
CHAPTERⅦExmples
Bibliography
Index