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Aubin T. — Nonlinear Analysis on Manifolds: Monge-Ampere Equations
Aubin T. — Nonlinear Analysis on Manifolds: Monge-Ampere Equations

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Название: Nonlinear Analysis on Manifolds: Monge-Ampere Equations

Автор: Aubin T.

Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1982

Количество страниц: 204

Добавлена в каталог: 21.04.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L_p$ spaces      78
A priori estimate      146 150—153 157 160—168 188
Absolutely continuous      77
Adjoint operator      27 75
Admissible function      141
Almost everywhere      76
Arc length      5
Ascoli’s Theorem      74
Atlas, classe $C^k$      1
Atlas, definition      1
Atlas, equivalent      1
Banach space      70
Banach — Steinhaus theorem      73
Banach’s theorem      74
Berger’s problem      119
Best constants      43 58 60 65 68
Best constants in Sobolev spaces      41 100 129
Best constants, definition      99
Betti numbers      29 30 142
Bianchi’s identities      6
Boundary      25
Bracket      2
Calabi’s conjecture      142 150
Calderon — Zygmund inequality      90
Cauchy’s Theorem      72
Chart      1
Chern class      140
Christoffel symbols      3
Clarkson’s inequalities      89
Closed      see Differentiable
Co-differential      27
Cohomology class, definition      140
Cohomology class, positive definite      142
Compact mapping      74
Complex manifold      139
Conjugate point      17 18
Connection      3
Connection, Riemannian      6
Continuity method      115 145 147 158 159
Convex ball      11 19
Convex function      159 174
Convex function, inequality for      178
Convex set      157
Convolution product      89
coordinates      1
Coordinates, geodesic      9
Coordinates, normal      7
Covariant derivative      4
Covering manifold      24
Critical point      40
Curvature, definition      3
Curvature, Ricci      7 140
Curvature, scalar      7
Curvature, sectional      7
Curvature, tensor      4 6 140
Cut locus      14 18
Degenerate      40
Density problem      33—35
Diffeomorphism      72
Differential operator      83
Differential operator, elliptic      83 84
Differential operator, leading part of      83
Differential operator, linear      83
Differential operator, uniformly elliptic      83
Differentiate      71
Differentiate form      2
Differentiate form, closed      28
Differentiate form, co-exact      28
Differentiate form, coclosed      28
Differentiate form, exact      28
Differentiate form, harmonic      28
Differentiate form, homologous      28
Differentiate, manifold      1
Differentiate, mapping      1
Dirichlet problem      157 158 182
Distance      5
Divergence form      85
Dual space      70
Eigenfunction      101 102
Eigenvalue, definition      75 102
Eigenvalue, of the Laplacian      31 101 102 134
Eigenvector      75
Einstein metric      7
Einstein — Kahler metric      143 146 150
Elliptic      see Differential operator and linear
Equicontinuous      74
Euler equation      42 102 103 120 122 123
Euler — Poincare characteristic X      29 120
Exact      28 see
Exceptional case      63 68
Exponential mapping      9
Exterior, differential p-form      2
Exterior, differentiation      3
Fatou’s theorem      77
First Chern class      140 143
First fundamental form      139
Fixed point method      115
FORM      see Differentiable
Formal adjoint      84
Fredholm nonlinear theorem      123
Fredholm theorem      75
Fubini’s Theorem      78
Functional      105 120 123 174 183
Gauss Bonnet theorem      120
Geodesic      8 11
Geodesic coordinates      9
Global scalar product      28
Green’s formula      107
Green’s function, definition      107
Green’s function, existence properties      108 112
Hahn — Banach theorem      73
Harmonic      see Differentiable Spherical
Hermitian metric      139
Hilbert space      70
Hodge decomposition theorem      29
Hoelder’s inequality      88
Homeomorphism      72
Homologous      28
Hopf — Rinow theorem      13
Imbedding      1
Immersion      1
Implicite function theorem      72
Improvement of the best constants      57 68
Index form      18
Index inequality      19
Inequality, Clarkson’s      89
Inequality, Hoelder’s      88
Inequality, index      19
Inequality, interpolation      93
Inequality, isoperimetric      40
Inequality, Minkowski      177
Inequality, optimal      50
Inequality, plurisubharmonic function      184 185
Injectivity radius      15
Inner product      70
Integrable      76
Integration over Riemannian manifolds      23 24 29
Interpolation inequalities      93
Inverse function theorem      72
Isoperimetric inequality      40
Jacobi field      17
Jacobian matrix      71
Kaehler, Einstein metric      143 146 150 see
Kaehler, manifold      139 140
Kaehler, metric      139 141
Kondrakov Theorem      53 55
Korn — Lichtenstein theorem      90
Kronecker’s symbol      4
Laplacian      27 106
Leading part      83
Lebesgue integral      75 77
Lebesgue measure      77
Lebesgue theorems      76 77
Length, arc      5
Length, minimizing      11
Length, second variation      15
Leray — Schauder theorem      74
Linear elliptic equation      101 113
Linear elliptic equation, existence of solution for      104 105 113
Linear mapping      70
Linear tangent mapping      2
Lower solution      97 see
Lower solution, method of      115 138 139 154 169
Manifold with boundary      25
Manifold, complete      13 14 16 45
Manifold, complex      139
Manifold, definition      1
Manifold, differentiable      1
Manifold, Riemannian      4
Mapping, differentiable      1
Mapping, rank      1
Maximum principle      96 97
Maximum principle, generalized      98
Mean value theorem      71
Measurable      76
Measure      76
METHODS      115
Metric, Einstein      7
Metric, Hermitian      139
Metric, Kaehler      139
Metric, Riemannian      4
Metric, space      5
Metric, tensor, estimates on      20
Minimizing curve      11
Monge — Ampere equation      144 157
Moser’s theorems      65 122
Myers’ theorem      16
Neumann problem      88
Nirenberg’s problem      122
Norm      70
Normal coordinates      7
Normed space      70
Open mapping theorem      73
Optimal inequalities      50
Orientable      23
Orientation      23
Parallel displacement      8
Parallel vector field      8
Parametrix for the Laplacian      106
Plurisubharmonic function      182
Plurisubharmonic function, inequality      184 185
Precompact      74
Projective space, complex      147 150
Projective space, real      23 122
Rademacker’s theorem      77
Radon measure      75 169 183
Radon’s theorem      81
Rank      71
Reflexive      70 81
Regularity up to the boundary      87
Regularity, interior      85 86
Regularization      80
Ricci curvature      7
Ricci form      140
Ricci tensor      7
Riemannian connection      6
Riemannian manifold      4
Riemannian metric      4
Scalar curvature      7
Schauder fixed point theorem      74
Schauder interior estimates      88
Second variation of the length integral      15
Sectional curvature      7
Semi-norm      73
Sense of distribution      84
Sobolev imbedding theorem      35 44 45 50
Sobolev imbedding theorem, proof      37—39 46 47 49 51
Sobolev lemma      37
Sobolev space      32
Spectrum      31
Spherical harmonic      133
Steepest descent      115
Subsolution      97 see
Supersolution      97 see Lower
Tangent space      2
Tangent vector      2
Taylor’s Formula      72
Tensor field      2
Topological methods      115
Torsion      3
Trace      69
Tubular neighborhood      15
Uniformly, convex      81
Uniformly, locally finite cover      48
Upper solution      97 see
Variational problem      42 101 105 115 116 119 120 126 179 185
Vector field      2
Volume element, oriented      26
Volume element, Riemannian      30
Weak, convergence      74
Weak, derivative      81 84
Weak, solution      84 85
Weakly sequentially compact      74
Weyl tensor      132
Whitney’s theorem      4
Yamabe’s equation      115
Yamabe’s problem      125
Yamabe’s theorem      126
Yang — Mills field      vii
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