Knowledge

Busemann's theorem

Source 📝

313: 205: 308: 200: 303: 277: 272: 110: 75: 33: 8: 79: 246: 219: 29: 251: 282: 241: 231: 37: 286: 91: 68: 297: 41: 255: 236: 99: 57: 17: 131: 65: 25: 263:
Gardner, Richard J. (2002). "The Brunn-Minkowski inequality".
220:"A theorem on convex bodies of the Brunn-Minkowski type" 40:in 1949 and was motivated by his theory of area in 295: 154: − 1)-dimensional volume of 47: 276: 245: 235: 217: 262: 187:forms the boundary of a convex body in 296: 13: 130: − 1)-dimensional 90: − 2)-dimensional 14: 325: 1: 287:10.1090/S0273-0979-02-00941-2 265:Bull. Amer. Math. Soc. (N.S.) 211: 224:Proc. Natl. Acad. Sci. U.S.A 7: 314:Theorems in convex geometry 271:(3): 355–405 (electronic). 206:PrĂŠkopa–Leindler inequality 194: 10: 330: 218:Busemann, Herbert (1949). 201:Brunn–Minkowski inequality 36:. It was first proved by 48:Statement of the theorem 309:Geometric inequalities 111:orthogonal complement 237:10.1073/pnas.35.1.27 34:geometric tomography 304:Euclidean geometry 30:Euclidean geometry 22:Busemann's theorem 321: 290: 280: 259: 249: 239: 38:Herbert Busemann 329: 328: 324: 323: 322: 320: 319: 318: 294: 293: 278:10.1.1.106.7344 214: 197: 166: 125: 92:linear subspace 74:containing the 69:Euclidean space 50: 12: 11: 5: 327: 317: 316: 311: 306: 292: 291: 260: 213: 210: 209: 208: 203: 196: 193: 171:be the curve { 162: 121: 49: 46: 42:Finsler spaces 9: 6: 4: 3: 2: 326: 315: 312: 310: 307: 305: 302: 301: 299: 288: 284: 279: 274: 270: 266: 261: 257: 253: 248: 243: 238: 233: 229: 225: 221: 216: 215: 207: 204: 202: 199: 198: 192: 190: 186: 182: 178: 174: 170: 165: 161: 158: âˆŠ  157: 153: 150:) to be the ( 149: 145: 141: 137: 133: 129: 124: 120: 116: 112: 108: 104: 101: 97: 93: 89: 85: 81: 77: 73: 70: 67: 63: 59: 55: 45: 43: 39: 35: 31: 27: 23: 19: 268: 264: 230:(1): 27–31. 227: 223: 188: 184: 180: 176: 172: 168: 163: 159: 155: 151: 147: 143: 139: 135: 127: 126:denote the ( 122: 118: 114: 106: 102: 95: 87: 83: 71: 61: 53: 51: 21: 15: 134:containing 100:unit vector 98:. For each 66:dimensional 58:convex body 18:mathematics 298:Categories 212:References 132:hyperplane 273:CiteSeerX 142:. Define 256:16588849 195:See also 183:. Then 80:interior 247:1062952 167:. Let 86:be an ( 78:in its 26:theorem 275:  254:  244:  179:)} in 117:, let 109:, the 82:. Let 76:origin 56:be a 24:is a 252:PMID 138:and 52:Let 32:and 283:doi 242:PMC 232:doi 113:of 105:in 94:of 60:in 28:in 16:In 300:: 281:. 269:39 267:. 250:. 240:. 228:35 226:. 222:. 191:. 173:θr 44:. 20:, 289:. 285:: 258:. 234:: 189:S 185:C 181:S 177:θ 175:( 169:C 164:θ 160:S 156:K 152:n 148:θ 146:( 144:r 140:S 136:θ 128:n 123:θ 119:S 115:S 107:S 103:θ 96:R 88:n 84:S 72:R 64:- 62:n 54:K

Index

mathematics
theorem
Euclidean geometry
geometric tomography
Herbert Busemann
Finsler spaces
convex body
dimensional
Euclidean space
origin
interior
linear subspace
unit vector
orthogonal complement
hyperplane
Brunn–Minkowski inequality
Prékopa–Leindler inequality
"A theorem on convex bodies of the Brunn-Minkowski type"
doi
10.1073/pnas.35.1.27
PMC
1062952
PMID
16588849
CiteSeerX
10.1.1.106.7344
doi
10.1090/S0273-0979-02-00941-2
Categories
Euclidean geometry

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

↑