478:
247:
137:. Historically, this lemma was first shown in the Hartogs domain in the case of two variables, also Oka's lemma is the inverse of the Levi's problem (unramified Riemann domain over
164:
69:
107:
131:
519:
538:
548:
166:). So maybe that's why Oka called Levi's problem as "problème inverse de Hartogs", and the Levi's problem is occasionally called
512:
287:
251:
543:
505:
336:(1953), "Sur les fonctions analytiques de plusieurs variables. IX. Domaines finis sans point critique intérieur",
398:
Noguchi, Junjiro (2019). "A brief chronicle of the Levi (Hartog's inverse) problem, coherence and open problem".
182:
110:
225:
485:
20:
438:
140:
45:
39:
463:
460:
425:
407:
322:
296:
207:
74:
489:
450:
417:
378:
345:
306:
260:
191:
359:
318:
274:
203:
355:
314:
270:
199:
134:
116:
532:
429:
326:
211:
383:
366:
219:
282:
333:
265:
35:
27:
421:
195:
310:
455:
350:
222:(2007), "The strong Oka's lemma, bounded plurisubharmonic functions and the
477:
180:
Harrington, Phillip S. (2007), "A quantitative analysis of Oka's lemma",
133:
is the distance to the boundary. This property shows that the domain is
412:
301:
283:"Oka's lemma, convexity, and intermediate positivity conditions"
400:
493:
16:
Theorem in mathematics about plurisubharmonic functions
228:
143:
119:
77:
48:
369:(1978), "Pseudoconvexity and the problem of Levi",
241:
158:
125:
101:
63:
439:"Domaines finis sans point critique intérieur"
513:
371:Bulletin of the American Mathematical Society
8:
19:For Oka's lemma about coherent sheaves, see
520:
506:
454:
411:
382:
349:
300:
264:
229:
227:
150:
146:
145:
142:
118:
76:
55:
51:
50:
47:
242:{\displaystyle {\overline {\partial }}}
281:Herbig, A.-K.; McNeal, J. D. (2012),
7:
474:
472:
492:. You can help Knowledge (XXG) by
231:
14:
476:
159:{\displaystyle \mathbb {C} ^{n}}
64:{\displaystyle \mathbb {C} ^{n}}
443:Japanese Journal of Mathematics
384:10.1090/S0002-9904-1978-14483-8
338:Japanese Journal of Mathematics
288:Illinois Journal of Mathematics
96:
90:
1:
539:Theorems in complex analysis
252:Asian Journal of Mathematics
234:
549:Mathematical analysis stubs
266:10.4310/AJM.2007.v11.n1.a12
565:
471:
422:10.4310/ICCM.2019.V7.N2.A2
102:{\displaystyle -\log d(z)}
18:
196:10.1007/s00209-006-0062-7
183:Mathematische Zeitschrift
218:Harrington, Phillip S.;
168:Hartogs' Inverse Problem
456:10.4099/jjm1924.23.0_97
351:10.4099/jjm1924.23.0_97
488:–related article is a
311:10.1215/ijm/1380287467
243:
160:
127:
103:
65:
486:mathematical analysis
437:Oka, Kiyoshi (1953),
295:(1): 195–211 (2013),
244:
161:
128:
104:
66:
21:Oka coherence theorem
226:
141:
117:
75:
46:
40:domain of holomorphy
249:-Neumann problem",
38:, states that in a
544:Lemmas in analysis
239:
156:
123:
99:
61:
501:
500:
344:: 97–155 (1954),
237:
126:{\displaystyle d}
556:
522:
515:
508:
480:
473:
459:
458:
433:
415:
387:
386:
362:
353:
329:
304:
277:
268:
248:
246:
245:
240:
238:
230:
214:
165:
163:
162:
157:
155:
154:
149:
132:
130:
129:
124:
111:plurisubharmonic
108:
106:
105:
100:
70:
68:
67:
62:
60:
59:
54:
564:
563:
559:
558:
557:
555:
554:
553:
529:
528:
527:
526:
469:
436:
397:
394:
392:Further reading
365:
332:
280:
224:
223:
217:
179:
176:
144:
139:
138:
115:
114:
73:
72:
71:, the function
49:
44:
43:
24:
17:
12:
11:
5:
562:
560:
552:
551:
546:
541:
531:
530:
525:
524:
517:
510:
502:
499:
498:
481:
467:
466:
434:
393:
390:
389:
388:
377:(4): 481–513,
363:
330:
278:
259:(1): 127–139,
236:
233:
215:
190:(1): 113–138,
175:
172:
153:
148:
122:
98:
95:
92:
89:
86:
83:
80:
58:
53:
15:
13:
10:
9:
6:
4:
3:
2:
561:
550:
547:
545:
542:
540:
537:
536:
534:
523:
518:
516:
511:
509:
504:
503:
497:
495:
491:
487:
482:
479:
475:
470:
465:
462:
457:
452:
448:
444:
440:
435:
431:
427:
423:
419:
414:
409:
405:
401:
396:
395:
391:
385:
380:
376:
372:
368:
367:Siu, Yum-Tong
364:
361:
357:
352:
347:
343:
339:
335:
331:
328:
324:
320:
316:
312:
308:
303:
298:
294:
290:
289:
284:
279:
276:
272:
267:
262:
258:
254:
253:
221:
220:Shaw, Mei-Chi
216:
213:
209:
205:
201:
197:
193:
189:
185:
184:
178:
177:
173:
171:
169:
151:
136:
120:
112:
93:
87:
84:
81:
78:
56:
41:
37:
33:
29:
22:
494:expanding it
483:
468:
446:
442:
406:(2): 19–24.
403:
399:
374:
370:
341:
337:
334:Oka, Kiyoshi
292:
286:
256:
250:
187:
181:
167:
135:pseudoconvex
34:, proved by
31:
25:
36:Kiyoshi Oka
32:Oka's lemma
28:mathematics
533:Categories
449:: 97–155,
413:1807.08246
174:References
430:119619733
327:118437110
302:1112.5138
235:¯
232:∂
212:121735220
85:
79:−
113:, where
360:0071089
319:3117025
275:2304586
204:2282262
428:
358:
325:
317:
273:
210:
202:
484:This
426:S2CID
408:arXiv
323:S2CID
297:arXiv
208:S2CID
490:stub
464:TeX
461:PDF
451:doi
418:doi
379:doi
346:doi
307:doi
261:doi
192:doi
188:256
109:is
82:log
42:in
26:In
535::
447:27
445:,
441:,
424:.
416:.
402:.
375:84
373:,
356:MR
354:,
342:23
340:,
321:,
315:MR
313:,
305:,
293:56
291:,
285:,
271:MR
269:,
257:11
255:,
206:,
200:MR
198:,
186:,
170:.
30:,
521:e
514:t
507:v
496:.
453::
432:.
420::
410::
404:7
381::
348::
309::
299::
263::
194::
152:n
147:C
121:d
97:)
94:z
91:(
88:d
57:n
52:C
23:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.