Knowledge (XXG)

Ohsawa–Takegoshi L2 extension theorem

Source 📝

369: 103: 536: 487: 429: 291: 62: 123: 137:, but simpler proofs have since been discovered. Many generalizations and similar results exist, and are known as theorems of Ohsawa–Takegoshi type. 661:
estimates for the d-bar operator on complex manifolds, Notes de cours, Ecole d'été de Mathématiques (Analyse Complexe), Institut Fourier, Grenoble"
581: 256: 696: 553: 691: 599:
Siu, Yum-Tong (2011). "Section extension from hyperbolic geometry of punctured disk and holomorphic family of flat bundles".
134: 37: 433: 21: 656: 670: 229: 345: 73: 79: 618: 33: 126: 634: 608: 587: 450: 392: 328: 320: 302: 216: 674: 577: 563: 549: 252: 626: 569: 541: 498: 442: 382: 312: 244: 206: 146: 514: 465: 407: 269: 40: 538:
Approaches in Several Complex Variables: Towards the Oka–Cartan Theory with Precise Bounds
622: 108: 66: 685: 638: 591: 454: 396: 332: 220: 125:) to a domain of higher dimension, with a bound on the growth. It was discovered by 70: 316: 248: 630: 573: 545: 502: 211: 194: 568:. Springer Proceedings in Mathematics & Statistics. Vol. 309. 2020. 16:
Result concerning the holomorphic extensions In several complex variables
324: 446: 387: 341: 489:
holomorphic functions VIII — a remark on a theorem of Guan and Zhou".
613: 307: 129:
and Kensho Takegoshi in 1987, using what have been described as
404:
Ohsawa, Takeo; Takegoshi, Kensho (1987). "On the extension of
293:
extension problem with an optimal estimate and applications".
243:. Progress in Mathematics. Vol. 188. pp. 47–82. 517: 468: 410: 348: 272: 266:
Guan, Qi'an; Zhou, Xiangyu (2015). "A solution of an
111: 82: 43: 530: 481: 423: 363: 285: 117: 97: 56: 165: 8: 342:"L estimates and existence theorems for the 462:Ohsawa, Takeo (2017). "On the extension of 65:-holomorphic function defined on a bounded 612: 522: 516: 473: 467: 415: 409: 386: 350: 349: 347: 306: 277: 271: 210: 110: 89: 85: 84: 81: 48: 42: 158: 32:is a fundamental result concerning the 671:Analytic Methods in Algebraic Geometry 565:Bousfield Classes and Ohkawa's Theorem 540:. Springer Monographs in Mathematics. 7: 491:International Journal of Mathematics 655:Demailly, Jean-Pierre (June 1996). 176: 510:Ohsawa, Takeo (10 December 2018). 364:{\displaystyle {\bar {\partial }}} 352: 195:"Cauchy–Riemann meet Monge–Ampère" 14: 230:"On the Ohsawa–Takegoshi–Manivel 199:Bulletin of Mathematical Sciences 98:{\displaystyle \mathbb {C} ^{n}} 355: 228:Demailly, Jean-Pierre (2000). 1: 241:Complex Analysis and Geometry 166:Ohsawa & Takegoshi (1987) 317:10.4007/annals.2015.181.3.6 249:10.1007/978-3-0348-8436-5_3 713: 135:Laplace–Beltrami operators 133:methods involving twisted 697:Several complex variables 631:10.1007/s11425-011-4293-7 601:Science China Mathematics 574:10.1007/978-981-15-1588-0 546:10.1007/978-4-431-55747-0 503:10.1142/S0129167X17400055 434:Mathematische Zeitschrift 212:10.1007/s13373-014-0058-2 193:Błocki, Zbigniew (2014). 22:several complex variables 431:holomorphic functions". 340:Hörmander, Lars (1965). 675:OpenContent book See B5 105:of dimension less than 532: 483: 425: 365: 287: 119: 99: 58: 692:Mathematical theorems 533: 531:{\displaystyle L^{2}} 484: 482:{\displaystyle L^{2}} 426: 424:{\displaystyle L^{2}} 366: 295:Annals of Mathematics 288: 286:{\displaystyle L^{2}} 120: 100: 59: 57:{\displaystyle L^{2}} 515: 466: 408: 346: 270: 109: 80: 41: 623:2011ScChA..54.1767S 528: 479: 447:10.1007/BF01166457 421: 388:10.1007/BF02391775 361: 283: 234:extension theorem" 115: 95: 54: 583:978-981-15-1587-3 358: 258:978-3-0348-9566-8 118:{\displaystyle n} 30:extension theorem 26:Ohsawa–Takegoshi 704: 667: 665: 642: 616: 607:(8): 1767–1802. 595: 559: 537: 535: 534: 529: 527: 526: 506: 488: 486: 485: 480: 478: 477: 458: 430: 428: 427: 422: 420: 419: 400: 390: 375:Acta Mathematica 370: 368: 367: 362: 360: 359: 351: 336: 310: 301:(3): 1139–1208. 292: 290: 289: 284: 282: 281: 262: 238: 224: 214: 179: 174: 168: 163: 147:Suita conjecture 124: 122: 121: 116: 104: 102: 101: 96: 94: 93: 88: 63: 61: 60: 55: 53: 52: 36:extension of an 712: 711: 707: 706: 705: 703: 702: 701: 682: 681: 680: 663: 654: 650: 645: 598: 584: 562: 556: 518: 513: 512: 509: 469: 464: 463: 461: 411: 406: 405: 403: 344: 343: 339: 273: 268: 267: 265: 259: 236: 227: 192: 188: 183: 182: 175: 171: 164: 160: 155: 143: 107: 106: 83: 78: 77: 44: 39: 38: 19: 17: 12: 11: 5: 710: 708: 700: 699: 694: 684: 683: 679: 678: 668: 651: 649: 648:External links 646: 644: 643: 596: 582: 560: 554: 525: 521: 507: 476: 472: 459: 441:(2): 197–204. 418: 414: 401: 357: 354: 337: 280: 276: 263: 257: 225: 205:(3): 433–480. 189: 187: 184: 181: 180: 169: 157: 156: 154: 151: 150: 149: 142: 139: 114: 92: 87: 67:Stein manifold 51: 47: 15: 13: 10: 9: 6: 4: 3: 2: 709: 698: 695: 693: 690: 689: 687: 676: 672: 669: 662: 660: 653: 652: 647: 640: 636: 632: 628: 624: 620: 615: 610: 606: 602: 597: 593: 589: 585: 579: 575: 571: 567: 566: 561: 557: 555:9784431568513 551: 547: 543: 539: 523: 519: 508: 504: 500: 496: 492: 474: 470: 460: 456: 452: 448: 444: 440: 436: 435: 416: 412: 402: 398: 394: 389: 384: 380: 376: 372: 338: 334: 330: 326: 322: 318: 314: 309: 304: 300: 296: 278: 274: 264: 260: 254: 250: 246: 242: 235: 233: 226: 222: 218: 213: 208: 204: 200: 196: 191: 190: 185: 178: 173: 170: 167: 162: 159: 152: 148: 145: 144: 140: 138: 136: 132: 128: 112: 90: 75: 72: 68: 64: 49: 45: 35: 31: 29: 23: 658: 604: 600: 564: 511: 494: 490: 438: 432: 378: 374: 298: 294: 240: 231: 202: 198: 172: 161: 130: 127:Takeo Ohsawa 71:pseudoconvex 27: 25: 18: 69:(such as a 34:holomorphic 686:Categories 381:: 89–152. 186:References 177:Siu (2011) 639:119572640 614:1104.2563 592:242194764 455:122156071 397:120051843 371:operator" 356:¯ 353:∂ 308:1310.7169 333:56205818 325:24523356 221:53582451 141:See also 619:Bibcode 76:set in 74:compact 637:  590:  580:  552:  453:  395:  331:  323:  255:  219:  131:ad hoc 24:, the 664:(PDF) 635:S2CID 609:arXiv 588:S2CID 497:(9). 451:S2CID 393:S2CID 329:S2CID 321:JSTOR 303:arXiv 237:(PDF) 217:S2CID 578:ISBN 550:ISBN 253:ISBN 153:note 627:doi 570:doi 542:doi 499:doi 443:doi 439:195 383:doi 379:113 313:doi 299:181 245:doi 207:doi 20:In 688:: 633:. 625:. 617:. 605:54 603:. 586:. 576:. 548:. 495:28 493:. 449:. 437:. 391:. 377:. 373:. 327:. 319:. 311:. 297:. 251:. 239:. 215:. 201:. 197:. 677:) 673:( 666:. 659:L 657:" 641:. 629:: 621:: 611:: 594:. 572:: 558:. 544:: 524:2 520:L 505:. 501:: 475:2 471:L 457:. 445:: 417:2 413:L 399:. 385:: 335:. 315:: 305:: 279:2 275:L 261:. 247:: 232:L 223:. 209:: 203:4 113:n 91:n 86:C 50:2 46:L 28:L

Index

several complex variables
holomorphic
L 2 {\displaystyle L^{2}}
Stein manifold
pseudoconvex
compact
Takeo Ohsawa
Laplace–Beltrami operators
Suita conjecture
Ohsawa & Takegoshi (1987)
Siu (2011)
"Cauchy–Riemann meet Monge–Ampère"
doi
10.1007/s13373-014-0058-2
S2CID
53582451
"On the Ohsawa–Takegoshi–Manivel L extension theorem"
doi
10.1007/978-3-0348-8436-5_3
ISBN
978-3-0348-9566-8
arXiv
1310.7169
doi
10.4007/annals.2015.181.3.6
JSTOR
24523356
S2CID
56205818
"L estimates and existence theorems for the ¯ {\displaystyle {\bar {\partial }}} operator"

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.