Knowledge (XXG)

Behnke–Stein theorem on Stein manifolds

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Behnke, H.; Stein, K. (1939). "Konvergente Folgen von Regularitätsbereichen und die Meromorphiekonvexität".
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Raghavan, Narasimhan (1960). "Imbedding of Holomorphically Complete Complex Spaces".
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The study of Riemann surfaces typically belongs to the field of
113:"Entwicklung analytischer Funktionen auf Riemannschen Flächen" 58:) on such a Riemann surface. It is a generalization of the 47:. In other words, it states that there is a nonconstant 291: 16:
For Behnke–Stein theorem on domains of holomorphy, see
82:, but the proof method uses the approximation by the 194:"The Behnke-Stein Theorem for Open Riemann Surfaces" 199:Proceedings of the American Mathematical Society 311: 88:Behnke–Stein theorem on domains of holomorphy 8: 318: 304: 211: 111:Heinrich Behnke & Karl Stein (1948), 103: 7: 272: 270: 290:. You can help Knowledge (XXG) by 14: 274: 159:American Journal of Mathematics 1: 80:one-variable complex analysis 347:Differential geometry stubs 60:Runge approximation theorem 23:In mathematics, especially 363: 269: 15: 337:Several complex variables 86:used in the proof of the 25:several complex variables 286:-related article is a 284:differential geometry 237:Mathematische Annalen 192:Simha, R. R. (1989). 117:Mathematische Annalen 52:holomorphic function 29:Behnke–Stein theorem 18:Behnke–Stein theorem 249:10.1007/BF01597355 129:10.1007/BF01447838 62:and was proved by 56:univalent function 299: 298: 84:polyhedron domain 354: 342:Riemann surfaces 320: 313: 306: 278: 271: 261: 260: 232: 226: 225: 215: 189: 183: 182: 154: 148: 147: 108: 92:Oka–Weil theorem 362: 361: 357: 356: 355: 353: 352: 351: 327: 326: 325: 324: 267: 265: 264: 234: 233: 229: 213:10.2307/2047046 191: 190: 186: 171:10.2307/2372949 156: 155: 151: 110: 109: 105: 100: 76: 74:Method of proof 64:Heinrich Behnke 41:Riemann surface 21: 12: 11: 5: 360: 358: 350: 349: 344: 339: 329: 328: 323: 322: 315: 308: 300: 297: 296: 279: 263: 262: 227: 206:(4): 876–880. 184: 165:(4): 917–934. 149: 102: 101: 99: 96: 75: 72: 45:Stein manifold 31:states that a 13: 10: 9: 6: 4: 3: 2: 359: 348: 345: 343: 340: 338: 335: 334: 332: 321: 316: 314: 309: 307: 302: 301: 295: 293: 289: 285: 280: 277: 273: 268: 258: 254: 250: 246: 242: 238: 231: 228: 223: 219: 214: 209: 205: 201: 200: 195: 188: 185: 180: 176: 172: 168: 164: 160: 153: 150: 146: 142: 138: 134: 130: 126: 122: 118: 114: 107: 104: 97: 95: 93: 89: 85: 81: 73: 71: 69: 65: 61: 57: 53: 50: 49:single-valued 46: 42: 38: 34: 30: 26: 19: 292:expanding it 281: 266: 240: 236: 230: 203: 197: 187: 162: 158: 152: 120: 116: 106: 77: 28: 22: 243:: 204–216. 123:: 430–461, 331:Categories 145:0038.23502 98:References 68:Karl Stein 257:123982856 137:122535410 70:in 1948. 33:connected 90:and the 222:2047046 179:2372949 39:(open) 37:compact 255:  220:  177:  143:  135:  35:, non- 27:, the 282:This 253:S2CID 218:JSTOR 175:JSTOR 133:S2CID 43:is a 288:stub 66:and 245:doi 241:116 208:doi 204:105 167:doi 141:Zbl 125:doi 121:120 333:: 251:. 239:. 216:. 202:. 196:. 173:. 163:82 161:. 139:, 131:, 119:, 115:, 94:. 319:e 312:t 305:v 294:. 259:. 247:: 224:. 210:: 181:. 169:: 127:: 54:( 20:.

Index

Behnke–Stein theorem
several complex variables
connected
compact
Riemann surface
Stein manifold
single-valued
holomorphic function
univalent function
Runge approximation theorem
Heinrich Behnke
Karl Stein
one-variable complex analysis
polyhedron domain
Behnke–Stein theorem on domains of holomorphy
Oka–Weil theorem
"Entwicklung analytischer Funktionen auf Riemannschen Flächen"
doi
10.1007/BF01447838
S2CID
122535410
Zbl
0038.23502
doi
10.2307/2372949
JSTOR
2372949
"The Behnke-Stein Theorem for Open Riemann Surfaces"
Proceedings of the American Mathematical Society
doi

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