Greene R.E., Wu H. — Function Theory on Manifolds Which Possess a Pole :: Электронная библиотека попечительского совета мехмата МГУ

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Greene R.E., Wu H. — Function Theory on Manifolds Which Possess a Pole

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Название: Function Theory on Manifolds Which Possess a Pole

Авторы: Greene R.E., Wu H.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1979

Количество страниц: 213

Добавлена в каталог: 15.08.2008

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Предметный указатель

$L^{2}$ estimates of $\bar{\partial}$       145—146
Ahlfors' generalized Schwarz lemma      81 86 112 131
Bergman kernel      142 175 178
Bergman metric      3 55 133
Bergman metric in terms of special basis      153 155
Bergman metric of CH manifolds      141ff
Bounded exhaustion functions      99
Bounded exhaustion functions, existence of subharmonic      101
Canonical bundle      158
CH manifolds (Cartan — Hadamard manifolds)      1 5 20 57 111
CH manifolds (Cartan — Hadamard manifolds), Bergman metric of      141ff
CH manifolds (Cartan — Hadamard manifolds), conditions for biholomorphism to $C^{n}$       180ff
Chern — Kobayashi volume generalization of Schwarz lemma      131
Complete hyperbolic manifolds      3 111 112 113
Complex Laplacian      12
Complex manifold (notations)      8—9
Complex normal coordinates      11 155 176
Complex structure of a 2-dimensional Riemannian manifold      89 120
Complex structure of a 2-dimensional Riemannian manifold, Milnor's theorem on      89 120
Complex structure of a 2-dimensional Riemannian manifold, Yang's theorem on      120
Complex structure tensor      10
Connection, Hermitian      11
Connection, Levi-Civita      11
Convex function      7 14
Convex function, strictly convex function      14
Curvature      5
Curvature of a Hermitian metric      85—86
Curvature of a pseudo-Hermitian metric      85
Curvature, holomorphic sectional      5 112 113 128
Curvature, Ricci      5 129
Divergence form (of a second order elliptic operator)      78
Domination by a weal model      43
Eberlein — O'Neill boundary      176
Elat metric      123
Exhaustion function      14
Exhaustion function, bounded      99
Exhaustion function, bounded subharmonic      101
Exponential mapping      1
Gauss' lemma      22
Geodesic polar coordinates      23 31
Green's identity      44
Harmonic functions      2—3 15
Harmonic functions, $L^{p}$ norm of      47
Harmonic functions, existence of bounded      116
Harmonic functions, mean value theorem for      48
Harnack inequality, Moser's      79
Hermitian metric      9 82 136
Hermitian metric on unit ball      136
hessian      7
Hessian comparison theorem      19—20 99
Hodge theory      7 17
Holomorphic convexity      200
Holomorphic functions      15 195
Holomorphic functions of minimal degree      195
Holomorphic functions, infinity of $L^{p}$ norm of      47
Holomorphic n-forms      141
Holomorphic n-forms, of slow growth in $L^{2}$ sense      182 184 188
Holomorphic n-forms, of slow growth in $L^{\infty}$ sense      184
Holomorphic n-forms, of slow growth, nonvanishing of      188
Holomorphic sectional curvature      82 83 84 112
Holomorphic tangent space      9
Hyperbolic manifold      82 84
Hyperbolic manifold, measure hyperbolic      134
Hyperbolic metric, infinitesmal      112
Hyperbolicity      81
Imbedding by harmonic functions      15
Imbedding by holomorphic functions      114
Imbedding of convex surfaces      69

Involutive isometry      116
Jacobi equation      26 29 30 33 55
Jacobi field      22 23 26
Kaehler form      9
Kaehler manifold      11 15 99
Kaehler manifold, holomorphic functions on, constancy implied by boundednes      57
Kaehler metric      11
Kernel form      142
Laplacian      1 7
Laplacian, comparison theorem      26—27
Laplacian, complex      12
Levi form      12 100
Levi form of functions of distance      32—33 35
Levi form, computation of      13—14
Levi problem, Grauert's solution of      14
Lu Qi-keng conjecture      178
Manifold with a pole      5
Measure hyperbolic      134
Models      2 24 69
Models, 2-dimensional      69
Moser's Harnack inequality      79
Normal coordinate system      8
Normal coordinate system, complex      11 155
Normal geodesic      6
Plurisubharmonic function      13 126
Poincare — Lelong equation      192
Pole      2 5
Pseudo-distance, Kobayashi      81 82
Pseudo-Hermitian metric      85 124 129
Pseudo-Hermitian metric, singular set of      85 129
Quasi-isometry      2 56
Quasi-isometry theorem for manifold with pole      56
Radial curvature      5 29—30 99 111 113 148
Radial curvature on a Kaehler manifold      32 35
Radial curvature, function of a model      30
Radial plane      5
Radial vector field      5
Rauch comparison theorem      20 52 75
Real form      9
Ricci curvature      5 129
Ricci form      158
Ricci tensor      11 12 129
Rotationally symmetric Hermitian metric      85
Schwarz lemma, generalized      86
Schwarz lemma, generalized, volume (Chern — Kobayashi)      131
Schwarz lemma, generalized, Yau's      176
Second variation formula      6
Singular set of a pseudo-Hermitian metric      85 129
Siu — Yau theorem on manifolds biholomorphic to $C^{n}$       180ff
Special basis (of $L^{2}$ holomorphic (n,0) forms)      147—148
Special basis (of $L^{2}$ holomorphic (n,0) forms), Bergman metric in terms of      153 155
Spherically symmetric metric      24
Stein manifold      14 15
Stokes' theorem      44
Strictly convex function      7
Strictly plurisubharmonic function      14
Strong pseudo-convexity      176
Strongly pseudoconvex domain      177
Sturm comparison theorem      40 41
Subharmonic function      8
Subharmonic function, sub-mean value theorem for      43
Symmetric Riemannian manifold (with respect to hypersurface)      116
Totally geodesic submanifold      25 116
Transversal vector field      6
Uniform ellipticity      79
Volume function      51—52
Volume function, estimates of      52—55
Weak model      24
Yau's generalized Schwarz lemma      176

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