Some Nonlinear Problems in Riemannian GeometryDuring the last few years, the field of nonlinear problems has undergone great development. This book consisting of the updated Grundlehren volume 252 by the author and of a newly written part, deals with some important geometric problems that are of interest to many mathematicians and scientists but have only recently been partially solved. Each problem is explained, up-to-date results are given and proofs are presented. Thus, the reader is given access, for each specific problem, to its present status of solution as well as to the most up-to-date methods for approaching it. The main objective of the book is to explain some methods and new techniques, and to apply them. It deals with such important subjects as variational methods, the continuity method, parabolic equations on fiber. |
Contents
I | 1 |
II | 2 |
III | 3 |
V | 4 |
VI | 5 |
VII | 6 |
IX | 8 |
X | 9 |
CXVI | 185 |
CXVII | 187 |
CXVIII | 188 |
CXIX | 191 |
CXX | 194 |
CXXI | 196 |
CXXII | 197 |
CXXIII | 204 |
XI | 13 |
XII | 15 |
XIII | 16 |
XIV | 17 |
XV | 18 |
XVI | 20 |
XVII | 23 |
XVIII | 25 |
XIX | 26 |
XXI | 27 |
XXII | 29 |
XXIII | 31 |
XXIV | 32 |
XXV | 33 |
XXVI | 35 |
XXVII | 37 |
XXVIII | 38 |
XXIX | 39 |
XXX | 44 |
XXXI | 50 |
XXXIII | 53 |
XXXIV | 55 |
XXXV | 56 |
XXXVI | 57 |
XXXVII | 61 |
XXXVIII | 63 |
XXXIX | 65 |
XL | 67 |
XLI | 69 |
XLII | 70 |
XLIII | 71 |
XLIV | 72 |
XLVI | 73 |
XLVII | 74 |
LI | 75 |
LIII | 76 |
LIV | 77 |
LVII | 78 |
LIX | 80 |
LX | 81 |
LXI | 83 |
LXII | 84 |
LXIII | 85 |
LXIV | 88 |
LXVI | 89 |
LXVIII | 90 |
LXX | 93 |
LXXI | 96 |
LXXII | 97 |
LXXIII | 98 |
LXXIV | 99 |
LXXV | 100 |
LXXVI | 101 |
LXXVII | 104 |
LXXVIII | 106 |
LXXX | 107 |
LXXXI | 108 |
LXXXII | 112 |
LXXXIII | 115 |
LXXXIV | 117 |
LXXXV | 119 |
LXXXVI | 123 |
LXXXVII | 125 |
LXXXVIII | 129 |
LXXXIX | 134 |
XC | 139 |
XCI | 145 |
XCII | 146 |
XCIII | 150 |
XCV | 152 |
XCVI | 157 |
XCVII | 160 |
XCVIII | 161 |
XCIX | 162 |
C | 164 |
CI | 166 |
CIII | 169 |
CIV | 171 |
CV | 172 |
CVI | 175 |
CVIII | 176 |
CIX | 178 |
CXI | 179 |
CXIII | 180 |
CXIV | 182 |
CXV | 183 |
CXXIV | 209 |
CXXV | 214 |
CXXVI | 216 |
CXXVII | 218 |
CXXVIII | 221 |
CXXIX | 223 |
CXXX | 227 |
CXXXI | 229 |
CXXXII | 230 |
CXXXIII | 231 |
CXXXIV | 232 |
CXXXV | 233 |
CXXXVI | 235 |
CXXXVII | 238 |
CXXXVIII | 241 |
CXXXIX | 243 |
CXL | 245 |
CXLI | 247 |
CXLIII | 248 |
CXLIV | 249 |
CXLV | 251 |
CXLVI | 252 |
CXLVII | 253 |
CXLVIII | 254 |
CXLIX | 255 |
CLI | 256 |
CLII | 257 |
CLIV | 258 |
CLVI | 259 |
CLVII | 260 |
CLVIII | 263 |
CLXI | 266 |
CLXII | 267 |
CLXIII | 269 |
CLXIV | 271 |
CLXV | 272 |
CLXVII | 273 |
CLXVIII | 274 |
CLXIX | 276 |
CLXX | 277 |
CLXXI | 278 |
CLXXII | 281 |
CLXXIII | 285 |
CLXXIV | 288 |
CLXXV | 289 |
CLXXVI | 290 |
CLXXVII | 291 |
CLXXVIII | 292 |
CLXXIX | 293 |
CLXXX | 296 |
CLXXXI | 301 |
CLXXXII | 306 |
CLXXXIV | 311 |
CLXXXV | 314 |
CLXXXVII | 315 |
CXC | 316 |
CXCI | 317 |
CXCII | 318 |
CXCIV | 321 |
CXCV | 322 |
CXCVII | 323 |
CXCIX | 324 |
CCI | 325 |
CCII | 326 |
CCIII | 327 |
CCIV | 330 |
CCV | 333 |
CCVI | 343 |
CCVII | 344 |
CCVIII | 345 |
CCIX | 346 |
CCX | 348 |
CCXI | 351 |
CCXII | 352 |
CCXIII | 354 |
CCXIV | 356 |
CCXV | 357 |
CCXVI | 359 |
CCXVII | 360 |
CCXVIII | 361 |
CCXIX | 365 |
CCXX | 375 |
389 | |
393 | |
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Common terms and phrases
according to Theorem Aubin ball belongs best constant bounded C.R. Acad C₁(M compact manifold compact Riemannian manifold conformal metric consider Const converges coordinates Corollary critical points defined Definition denote derivatives diffeomorphism Dirichlet eigenvalue Einstein-Kähler metric elliptic equations exists a constant finite function f G-invariant geodesic Green function H₁ harmonic maps Hebey Hence Hölder's inequality implies injectivity radius integral Kähler manifold Kähler metric Kazdan Laplacian Lemma Let f locally conformally flat manifold of dimension Math maximum principle method metric g minimizing Moreover neighbourhood Nirenberg nonlinear norm open set point of concentration positive solution Proposition prove real number result Ricci curvature Riemannian manifold Riemannian metric satisfies scalar curvature sectional curvature sequence Sobolev imbedding theorem solve sphere strictly positive suppose symmetric tensor uniformly unique vanish Yamabe problem yields zero