LEADER 06374nam 22005895 450 001 9910154743803321 005 20230808192324.0 010 $a1-4008-8191-9 024 7 $a10.1515/9781400881918 035 $a(CKB)3710000000631378 035 $a(SSID)ssj0001651325 035 $a(PQKBManifestationID)16425720 035 $a(PQKBTitleCode)TC0001651325 035 $a(PQKBWorkID)13226588 035 $a(PQKB)11125706 035 $a(MiAaPQ)EBC4738612 035 $a(DE-B1597)467970 035 $a(OCoLC)979579219 035 $a(DE-B1597)9781400881918 035 $a(EXLCZ)993710000000631378 100 $a20190708d2016 fg 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 00$aSeminar on Differential Geometry. (AM-102), Volume 102 /$fShing-tung Yau 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2016] 210 4$d©1982 215 $a1 online resource (721 pages) 225 0 $aAnnals of Mathematics Studies ;$v279 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-691-08296-0 311 $a0-691-08268-5 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tTABLE OF CONTENTS -- $tINTRODUCTION -- $tSURVEY ON PARTIAL DIFFERENTIAL EQUATIONS IN 3 DIFFERENTIAL GEOMETRY / $rYau, Shing-Tung -- $tPOINCARÉ INEQUALITIES ON RIEMANNIAN MANIFOLDS / $rLi, Peter -- $tBONNESEN-TYPE INEQUALITIES IN ALGEBRAIC GEOMETRY, I: INTRODUCTION TO THE PROBLEM / $rTeissier, B. -- $tLIOUVILLE THEOREMS FOR HARMONIC MAPPINGS, AND AN APPROACH TO BERNSTEIN THEOREMS / $rHildebrandt, Stefan -- $tSUBHARMONIC FUNCTIONS, HARMONIC MAPPINGS AND ISOMETRIC IMMERSIONS / $rKarp, Leon -- $tAN ISOPERIMETRIC INEQUALITY AND WIEDERSEHEN MANIFOLDS / $rKazdan, Jerry L. -- $tON THE BLASCHKE CONJECTURE / $rYang, C. T. -- $tBEST CONSTANTS IN THE SOBOLEV IMBEDDING THEOREM THE Y AMABE PROBLEM / $rAubin, Thierry -- $tGAUSSIAN AND SCALAR CURVATURE, AN UPDATE / $rKazdan, Jerry L. -- $tCONFORMAL METRICS WITH ZERO SCALAR CURVATURE AND A SYMMETRIZATION PROCESS VIA MAXIMUM PRINCIPLE / $rNi, Wei-Ming -- $tRIGIDITY OF POSITIVELY CURVED MANIFOLDS WITH LARGE DIAMETER / $rGromoll, Detlef / Grove, Karsten -- $tCOMPLETE THREE DIMENSIONAL MANIFOLDS WITH POSITIVE RICCI CURVATURE AND SCALAR CURVATURE / $rSchoen, Richard / Yau, Shing-Tung -- $tENTIRE SPACELIKE HYPERSURFACES OF CONSTANT MEAN CURVATURE IN MINKOWSKI SPACE / $rTreibergs, Andrejs E. -- $tAPPLICATIONS OF THE MONGE-AMPERE OPERATORS TO THE DIRICHLET PROBLEM FOR QUASILINEAR ELLIPTIC EQUATIONS / $rBakelman, I. -- $tEXTREMAL KÄHLER METRICS / $rCalabi, Eugenio -- $tL2 HARMONIC FORMS ON COMPLETE MANIFOLDS / $rDodziuk, Jozef -- $tL2-COHOMOLOGY AND INTERSECTION HOMOLOGY OF SINGULAR ALGEBRAIC VARIETIES / $rCheeger, Jeff / Goresky, Mark / MacPherson, Robert -- $tFUNCTION THEORY OF NONCOMPACT KÄHLER MANIFOLDS OF NONPOSITIVE CURVATURE / $rGreene, R. E. -- $tKÄHLER MANIFOLDS WITH VANISHING FIRST CHERN CLASS / $rMichelsohn, M. L. -- $tCOMPACTIFICATION OF NEGATIVELY CURVED COMPLETE KAHLER MANIFOLDS OF FINITE VOLUME / $rSiu, Yum-Tong / Yau, Shing-Tung -- $tLOCAL ISOMETRIC EMBEDDINGS / $rJacobowitz, H. -- $tYANG-MILLS THEORY: ITS PHYSICAL ORIGINS AND DIFFERENTIAL GEOMETRIC ASPECTS / $rBourguignon, Jean Pierre / Lawson, H. Blaine -- $tSYMMETRY AND ISOLATED SINGULARITIES OF CONFORMALLY FLAT METRICS AND OF SOLUTIONS OF THE YANG-MILLS EQUATIONS / $rGidas, Basilis -- $tON PARALLEL YANG-MILLS FIELDS / $rChaohao, Gu -- $tVARIATIONAL PROBLEMS FOR GAUGE FIELDS / $rUhlenbeck, Karen K. -- $tSOME GEOMETRICAL ASPECTS OF INTEGRABLE NONLINEAR EVOLUTION EQUATIONS / $rChen, Hsing-Hen / Lee, Yee-Chun -- $tTHE CONFORMALLY INVARIANT LAPLACIAN AND THE INSTANTON VANISHING THEOREM / $rWells, R. O. -- $tCAUSALLY DISCONNECTING SETS, MAXIMAL GEODESICS AND GEODESIC INCOMPLET-ENESS FOR STRONGLY CAUSAL SPACE-TIMES / $rBeem, John K. / Ehrlich, Paul E. -- $tRENORMALIZATION / $rJaffe, Arthur -- $tMETRICS WITH PRESCRIBED RICCI CURVATURE / $rDeTurck, Dennis M. -- $tBLACK HOLE UNIQUENESS THEOREMS IN CLASSICAL AND QUANTUM GRAVITY / $rLapedes, A. S. -- $tGRAVITATIONAL INSTANTONS / $rPerry, Malcolm J. -- $tSOME UNSOLVED PROBLEMS IN CLASSICAL GENERAL RELATIVITY / $rPenrose, R. -- $tPROBLEM SECTION / $rYau, Shing-Tung -- $tBackmatter 330 $aThis collection of papers constitutes a wide-ranging survey of recent developments in differential geometry and its interactions with other fields, especially partial differential equations and mathematical physics. This area of mathematics was the subject of a special program at the Institute for Advanced Study in Princeton during the academic year 1979-1980; the papers in this volume were contributed by the speakers in the sequence of seminars organized by Shing-Tung Yau for this program. Both survey articles and articles presenting new results are included. The articles on differential geometry and partial differential equations include a general survey article by the editor on the relationship of the two fields and more specialized articles on topics including harmonic mappings, isoperimetric and Poincaré inequalities, metrics with specified curvature properties, the Monge-Arnpere equation, L2 harmonic forms and cohomology, manifolds of positive curvature, isometric embedding, and Kraumlhler manifolds and metrics. The articles on differential geometry and mathematical physics cover such topics as renormalization, instantons, gauge fields and the Yang-Mills equation, nonlinear evolution equations, incompleteness of space-times, black holes, and quantum gravity. A feature of special interest is the inclusion of a list of more than one hundred unsolved research problems compiled by the editor with comments and bibliographical information. 410 0$aAnnals of mathematics studies ;$vNumber 102. 606 $aGeometry, Differential 606 $aDifferential equations, Partial 615 0$aGeometry, Differential. 615 0$aDifferential equations, Partial. 676 $a516.36 686 $aSI 830$2rvk 702 $aYau$b Shing-tung, 712 02$aInstitute for Advanced Study (Princeton, N.J.) 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910154743803321 996 $aSeminar on Differential Geometry. (AM-102), Volume 102$92839544 997 $aUNINA