几何与分析（第1卷）

图书标准信息

• 作者 季理真 编
• 出版社 高等教育出版社
• 出版时间 2010-09
• 版次 1
• ISBN 9787040302721
• 定价 88.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 542页
• 正文语种 英语

【内容简介】

Thisbookcontainsmanysubstantialpapersfromdistinguishedspeakersofaconference"GeometricAnalysis:PresentandFuture"andanoverviewoftheworksofProfessorShing-TungYau.ContributorsincludeE.Wit-ten,Y.T.Siu,R.Hamilton,H.Hitchin,B.Lawson,A.Strominger,C.Vafa,W.Schmid,V.Guillemin,N.Mok,D.Christodoulou.Thisisavaluablereferencethatgivesanup-to-datedsummaryofgeometricanalysisanditsapplicationsinmanydifferentareasofmathematics.

【目录】

part1summaryofandcommentariesontheworkofshing-tungyau
curriculumvitaeofshing-tungyau
abriefoverviewoftheworkofshing-tungyau
lizhenji
1introduction
2asummaryofsomemajorworksofyau
3topicsyauhasworkedon
4basicsonkaihler-einsteinmetricsandcalabiconjectures
5someapplicationsofkaihler-einsteinmetricsandcalabi-yaumanifolds
6harmonicmaps
7rigidityofkahlermanifolds
8super-rigidityofspacesofnonpositivecurvature
9surveypapersbyyau
10openproblemsbyyau
llbookswrittenandco-writtenbyyau
12bookseditedandco-editedbyyau
13ph.d.studentsofyau
14partiallistofpapersandbooksofyau
references
yau'sworkonfilteringproblem

.wen-linchiou,jiehuangandlizhenji
1filteringproblem
2yau'stwomethodsinsolvingnonlinearfilteringproblem
2.1directmethod
2.2algorithmforrealtimesolutionwithoutmemory
references
fromcontinuestodiscrete-yau'sworkongraphtheory
fanchung
yau'sworkonmoduli,periods,andmirrormapsforcalabi-yaumanifolds
charlesf.doran
1constructionofcalabi-yauthreefolds
2picard-fuchsequationsandthemirrormap
3arithmeticpropertiesofmirrormaps
4periodsandmoduliofcomplextoriandk3surfaces
references
reviewonyau'sworkonthecoupledeinsteinequationsandthewavedynamicsinthekerrgeometry
felixfinster
1couplingtheeinsteinequationstonon-abeliangaugefieldsanddiracspinors
2thedynamicsoflinearwavesinthekerrgeometry
references
theworkofwittenandyauontheads/cftcorrespondence
gregoryj.galloway
1introduction
2thewitten-yauresultsonads/cft
3furtherdevelopments
references
yau'sworkonheatkernels
alexandergrigor'yan
1thenotionoftheheatkernel
2estimatingheatkernels
3someapplicationsoftheheatkernelestimates
references
yau'scontributionstoengineeringfields
xianfengdavidgu
1introduction
2computationalconformalgeometry
2.1conformalstructure
2.2harmonicmap
2.3surfacericciflow
2.4conformalmappings
2.5quasi-conformalmappings
2.6teichmiillerspace
3geometricacquisition
4computergraphics
5geometricmodeling
6medicalimaging
7computervision
8wirelesssensornetwork
9summary
references
thesyzproposal
naichungconanleung
1pre-syz
2thebirthofsyz
3thegrowingupofsyz
3.1speciallagrangiangeometry
3.2speciallagrangianfibrations
3.3affinegeometry
3.4syztransformation
4futureofsyz
references
yau-zaslowformula
naichungconanleung
yau'sworkonfunctiontheory:harmonicfunctions,eigenvaluesandtheheatequation
peterli
avisionofyauonmirrorsymmetry
bonglian
1enumerativegeometry
2geometryofcalabi-yaumanifoldsandtheirmodulispaces
references
yau'sworkongroupactions
kefengliu
chengandyau'sworkonthemonge-ampereequationandaffinegeometry
johnloftin,xu-jiawanganddeaneyang
1introduction
2themonge-ampereequation
3chengandyau'sworkonthedirichletproblem
4subsequentworkonthemonge-ampereequation
5affinespheres
6hyperbolicaffinespheresandrealmonge-ampereequations
7affinemanifolds
8maximalhypersurfacesinminkowskispace
9theminkowskiproblem
10convexgeometrywithoutsmoothnessassumptions
10.1supportfunction
10.2invariancepropertiesofthesupportfunction
10.3minkowskisum
10.4mixedvolume
10.5surfaceareameasure
10.6invariancepropertiesofthesurfaceareameasure
10.7theminkowskiproblem
10.8thebrunn-minkowskiinequality
10.9uniquenessintheminkowskiproblem
10.10variationalapproachtotheminkowskiproblem
11convexgeometrywithsmoothnessassumptions
11.1theinversegaussmap
11.2theinversesecondfundamentalform
11.3thecurvaturefunction
11.4thesurfaceareameasure
11.5theminkowskiproblem
11.6theminkowskiproblemasapde
12chengandyau'sregularitytheoremfortheminkowskiproblem.
12.1statement
12.2sketchofproof
13generalizationsoftheminkowskiproblem
references
yau'sworkonminimalsurfacesand3-manifolds
fengluo
theworkofschoenandyauonmanifoldswithpositivescalarcurvature
william,minicozziii
0introduction
1topologicalrestrictionsonmanifoldswithpositivescalarcurvature
1.1stableminimalsurfacesandscalarcurvature
1.2inductivelyextendingthistohigherdimensions
1.3preservingpositivescalarcurvatureundersurgery
2locallyconformallyflatmanifolds
2.1thenewinvariants
2.2apositivemasstheorem
references
yau'scontributionstoalgebraicgeometryndreytodorov
1introduction
1.1yau'sprogram-plenarytalkaticm1982
2monge-ampereequationandapplicationstoalgebraicgeometry
2.1solutionofthecalabiconjecture
2.2existenceofcanonicalmetricsonzariskiopensets
3stablevectorbundlesoverkahlermanifolds
3.1donaldson-uhlenbeek-yautheorem
3.2applicationstokodaira'sclassificationofsurfaces
4modulispaces
4.1existenceofkiihler-einsteinmetricsondomainofholomorphyandteichmfillerspaces
4.2modulispacesofk3surfaces
4.3modulispacesofcymanifolds
4.4generalizationofshwarzlemmabyyauandbaily-borelcompactification
5contributionsofyautostringtheory
5.1mirrorsymmetryandsyzconjecture
5.2largeradiuslimit
5.3stringtheoryandnumbertheory
5.4rationalcurvesonalgebraick3surfaces
6rigidity
6.1yau'sconjectureaboutrigidityofsomecomplexmanifolds
6.2geometricproofofmargulis'superrigidity
6.3geometricproofofkazhdantheoremaboutgalois
conjugationofshimuravarieties
references
yau'sworkonpositivemasstheorems
mu-taowang
yan'sconjectureonkaihler-einsteinmetricandstability
xiaoweiwang
onyau'spioneercontributiononthefrankelconjectureand
relatedquestions
fangyangzheng
yau'sworkoninequalitiesbetweenchernnumbersand
uniformizationofcomplexmanifolds
kangzuo
part2differentialgeometryanddifferentialequations
geometryofcompletegradientshrinkingriccisolitons
huai-dongcao
1gradientshrinkingriccisolitons
2classificationof3-dimensionalgradientshrinkingsolitons
3geometryofcompletegradientsolitons
references
theformationofblackholesingeneralrelativity
demetrioschristodoulou
pagerankasadiscretegreen'sfunction
fanchung
1introduction
2preliminaries
3dirichleteigenvalues
4connectionsbetweenpagerankanddiscretegreen'sfunction
5relatingthecheegerconstanttothepagerank
6relatingthepagerankofagraphtothatofitssubgraphs
7thepagerankandthehittingtime
references
ageodesicequationinthespaceofsasakianmetrics
pengfeiguanandxizhang
someinversespectralresultsforthetwo-dimensionalschrodingeroperator
v.cuilleminanda.uribe
1introduction
2theweylcalculus
3somebracketidentities
4thequantumbirkhoffcanonicalform
references
li-yauestimatesandtheirharnackinequalities
richards.hamilton
1theheatequation
2thedirichletproblemfortheheatequation
3theheatequationintheplane
4thecastaway
5endangeredspeciesequation
6themigrationequation
7motionofacurvebyitscurvature
8motionofasurfacebyitsmeancurvature
9motionofasurfacebyitsgausscurvature
references
plurisubharmonicityinageneralgeometriccontext
f.reeseharveyandh.blainelawson,jr
1introduction
2geometricallydefinedplurisubharmonicfunctions
3moregeneralplurisubharmonicfunctionsdefinedbyanellipticconep+
4p+-plurisubharmonicdistributions
5upper-semi-continuousp+-plurisubharmonicfunctions
6someclassicalfactsthatextendtop+-plurisubharmoniefunctions
7thedirichletproblemuniqueness
8thedirichletproblemexistence
9p+-convexdomains
10topologicalrestrictionsonp+-convexdomains
11p+-freesubmanifolds
12p+-convexboundaries
references
poissonmodulesandgeneralizedgeometry
nigelhitchin
1introduction
2poissonmodules
2.1definitions
2.2aconstruction
3theserreconstruction
3.1thealgebraicapproach
3.2theanalyticalapproach
3.3thesecondsection
4generalizedgeometry
4.1basicfeatures
4.2generalizeddolbeaultoperators
4.3thecanonicalbundle
5ageneralizedconstruction
5.1theproblem
5.2generalizedcomplexsubmanifolds
5.3theconstruction
6anapplication
references
uniquenessofsolutionstomeanfieldequationsofliouvilletypeintwo-dimension
chang-shoulin
1introduction
2uniquenessinr2
3uniquenessinboundeddomainsofr2
4onofriinequalityanditsgeneralization
5meanfieldequationandgreenfunctionsontorus
6generalizedliouvillesystem
references
monotonicityandholomorphicfunctions
leini
decayofsolutionstothecauchyprobleminthekerrgeometryforvariousphysicalsystems:stabilityofblackholes
j.a.smoller
1introduction
2main
references
thecalabi-yauequation,symplecticformsandalmostcomplexstructures
valentinotosattiandbenweinkove
1background-yau'stheorem
2donaldson'sconjectureandapplications
3estimatesforthecatabi-yauequation
4methods
5amonotonicityformula
references
understandingweil-peterssoncurvature
scotta.wolpert
1introduction
2basicsofteichmiillertheory
3wpintrinsicgeometry
4methods
5applicationsofcurvature
5.1theworkofliu,sunandyau
5.2themodelmetric4dr2+rsdo2
5.3projectionanddistancetoastratum
references
examplesofpositivelycurvedcompletekahlermanifolds
hung-hsiwuandfangyangzheng
1introduction
2theabcdfunctions
3characterizationbythefunction
4someexamples
5characterizationbysurfaceofrevolution
6correlationbetweenvolumegrowthandcurvaturedecay
references