Eliashberg Y., Mishachev N. — Introduction to the h-Principle :: Электронная библиотека попечительского совета мехмата МГУ

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Eliashberg Y., Mishachev N. — Introduction to the h-Principle

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Название: Introduction to the h-Principle

Авторы: Eliashberg Y., Mishachev N.

Аннотация:

Eliashberg and Mishachev (credentials not listed) discuss two methods for proving the h-principle: holonomic approximation and convex integration. Applications to symplectic and contact geometry are emphasized. A brief text, the book is suited for a graduate-level course on geometric methods for solving partial differential equations and inequalities. Numerous diagrams illustrate the principles and concepts described in the text.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 216

Добавлена в каталог: 02.06.2005

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Предметный указатель

$d_g(f,\tilde f)$       184
      10
$J^r(\mathbb R^n,\mathbb R^q)$       8
      8
-mersion      62
      159
      9
      10
      9
$P_{t,y}$       148
$p_{\mathcal J}$       73
$p_{\mathcal S}$       73
$r(\tilde g,g)$       183
$S^{\perp_\omega}$       70
$X^{(r)}$       9
$\Lambda^pV$       72
$\mathbb S^+_{\mathrm{cont}}$       94
$\mathbb S^a_{\mathrm{non-deg}}$       97
$\mathbb S^a_{\mathrm{symp}}$       93
$\mathbb S_{\mathrm{cont}}$       94
$\mathbb S_{\mathrm{symp}}$       93
$\mathcal H(L)$       73
$\mathcal H(X)$       74
$\mathcal J$       93
$\mathcal J(L)$       72
$\mathcal J(X)$       74
$\mathcal L_X$       79
$\mathcal O_pA$       9
$\mathcal R^\varepsilon_{\mathrm{coisot}}$       167
$\mathcal R^\varepsilon_{\mathrm{comp}}$       168
$\mathcal R^\varepsilon_{\mathrm{isot}}$       167
$\mathcal R^\varepsilon_{\mathrm{Lag}}$       167
$\mathcal R_A$       165
$\mathcal R_{k-\mathrm{mers}}$       160
$\mathcal R_{\mathrm{clo}}$       49
$\mathcal R_{\mathrm{coisot}}$       166
$\mathcal R_{\mathrm{comp}}$       168
$\mathcal R_{\mathrm{cont}}$       87
$\mathcal R_{\mathrm{coreal}}$       168
$\mathcal R_{\mathrm{hol}}$       126
$\mathcal R_{\mathrm{imm-trans}}$       131
$\mathcal R_{\mathrm{imm}}$       48
$\mathcal R_{\mathrm{isocont}}$       87
$\mathcal R_{\mathrm{isosymp}}$       124
$\mathcal R_{\mathrm{isot}}$       166
$\mathcal R_{\mathrm{Lag}}$       124 166
$\mathcal R_{\mathrm{Leg}}$       87
$\mathcal R_{\mathrm{real}}$       168
$\mathcal R_{\mathrm{sub-isotr}}$       124
$\mathcal R_{\mathrm{sub}}$       48
$\mathcal R_{\mathrm{symp}}$       166
$\mathcal R_{\mathrm{tang}}$       130
$\mathcal R_{\mathrm{trans}}$       130
$\mathcal S(L)$       70
$\mathcal S(X)$       74
$\mathcal S^+_{\mathrm{cont}}$       94
$\mathcal S_{\mathrm{cont}}$       94
$\mathcal S_{\mathrm{non-deg}}$       97
$\mathcal S_{\mathrm{symp}}$       93
$\mathrm{bf}F$       11
$\mathrm{Clo}_a\mathcal R$       94
$\mathrm{Conn}_y\Omega$       148
$\mathrm{Conv}\mathcal R$       149
$\mathrm{Conv}_F\mathcal R$       149
$\mathrm{CS}(\xi)$       83
$\mathrm{Exa}\mathcal R$       96
$\mathrm{Gr}_nW$       37
$\mathrm{G}F, \mathrm{G}df,$       37
$\mathrm{Hol}X^{(r)}$       11
$\mathrm{Sec}X^{(r)}$       11
$\Omega(t,y)$       148
$\theta$ -pair      125
Almost complex structure      75
Almost complex structure, integrable      75
Almost symplectic structure      75
Almost symplectic structure, integrable      75
Ampleness criterion      165
Balanced path      152
Canonical symplectic structure (form) on $\mathbb R^{2n}$       76
Canonical symplectic structure (form) on a cotangent bundle      77
Capacious Lie subgroup      133
Characteristic foliation      76
Compatible complex and symplectic structures      73
Complex manifold      75 76
Complex structure      71
Complex subspace      72
Complex vector space      71
Contact cutting-off      92
Contact distribution      82
Contact form      82
Contact Hamiltonian      92
Contact manifold      82
Contact monomorphism      87
Contact structure      4 82
Contact structure, cooriented      83
Contact structure, overtwisted      102
Contact structures, formally homotopic      102
Contact structures, homotopic      102
Contact structures, isotopic      102
Contact vector field      92
Contactization      84
Contactomorphisms      83
Convex integration      XII
Convex integration, iterated      160
Convex integration, one-dimensional      149
Convex integration, parametric      155
Coordinate principal subspace      159 162
CR-structure      76
Darboux contact form      82
Darboux' chart      76
Diffeotopy, $\delta$ -small      20
Differential condition      47
Differential inclusion      148
Differential relation      XI 47
Differential relation, -flexible      126
Differential relation, -microflexible      125 126
Differential relation, $\mathfrak A$ -invariant      133
Differential relation, ample      148 163
Differential relation, ample in the coordinate directions      159
Differential relation, closed      49
Differential relation, determined      XI 49
Differential relation, Diff V-invariant      60
Differential relation, fibered      58
Differential relation, fiberwise path-connected      149
Differential relation, locally integrable      123 124
Differential relation, microflexible      126
Differential relation, open      49
Differential relation, overdetermined      49
Differential relation, underdetermined      XI 49
distribution      42
Embedding, $\varepsilon$ -Lagrangian      3
Embedding, co-real      170
Embedding, contact      115
Embedding, directed      168
Embedding, isocontact      115
Embedding, isosymplectic      105
Embedding, Lagrangian      3
Embedding, real      3 170
Embedding, symplectic      105
Engel structure      4
Epimorphism      48
Exact Lagrangian immersion      89
Exact Lagrangian submanifold      89
Exact symplectic manifold      140
Family of sections      7
Family of sections, continuous      7
Family of sections, smooth      7
Fiber bundle      7
Fibered map      58
Fibration      7

Fibration, natural      59
Fibration, trivial      7
Flower      151
Flower, abstract      150
Flower, fibered      155
Formal inverse      172
Formal primitive      43
Formal primitive, Hamiltonian function      91
Formal primitive, time dependent      91
Hamiltonian isotopy      91
Hermitian structure      73 75
Hermitian structure, integrable      75
Holonomic $\mathcal R$ -approximation theorem      127
Holonomic approximation      19
Holonomic approximation theorem      20
Homotopy principle (h-principle)      XI 2 54
Homotopy principle (h-principle) for $\mathcal C^1$ -isometric immersions      182
Homotopy principle (h-principle) for $\mathcal D$ -sections      172
Homotopy principle (h-principle) for ample differential relations      163
Homotopy principle (h-principle) for contact structures on open manifolds      96
Homotopy principle (h-principle) for differential relations over a cube      162
Homotopy principle (h-principle) for directed embeddings      168
Homotopy principle (h-principle) for divergence free vector fields      174
Homotopy principle (h-principle) for generalized isocontact immersions      139
Homotopy principle (h-principle) for generalized isosymplectic immersions      143
Homotopy principle (h-principle) for immersions transversal to contact distribution      131
Homotopy principle (h-principle) for immersions transversal to distribution      65
Homotopy principle (h-principle) for isocontact embeddings      115
Homotopy principle (h-principle) for isocontact immersions      137
Homotopy principle (h-principle) for isosymplectic embeddings      106
Homotopy principle (h-principle) for isosymplectic immersions      142
Homotopy principle (h-principle) for Lagrangian immersions      140
Homotopy principle (h-principle) for Legendrian immersions      138
Homotopy principle (h-principle) for maps transversal to contact distribution      130
Homotopy principle (h-principle) for maximally non-integrable tangent hyperplane distributions on even-dimensional manifold      132 178
Homotopy principle (h-principle) for microflexible $\mathfrac A$ -invariant relations      134
Homotopy principle (h-principle) for microflexible Diff V-invariant relations      128
Homotopy principle (h-principle) for non-vanishing $\mathcal D$ -sections      173
Homotopy principle (h-principle) for open Diff V-invariant relations      60
Homotopy principle (h-principle) for real and co-real embeddings      170
Homotopy principle (h-principle) for real and co-real immersions      168
Homotopy principle (h-principle) for sections transversal to distribution      65
Homotopy principle (h-principle) for subcritical isotropic embeddings      122
Homotopy principle (h-principle) for symplectic structures on open manifolds      95
Homotopy principle (h-principle) for systems of divergence free vector fields      176
Homotopy principle (h-principle) for systems of exact forms      176
Homotopy principle (h-principle) for systems of linearly-independent $\mathcal D$ -sections      174
Homotopy principle (h-principle) for two-forms of maximal rank on odd-dimensional manifolds      97 177
Homotopy principle (h-principle), -dense      58
Homotopy principle (h-principle), (multi) parametric      56
Homotopy principle (h-principle), fibered      58
Homotopy principle (h-principle), local      57
Homotopy principle (h-principle), one-parametric      54
Homotopy principle (h-principle), relative      57
Homotopy principle (h-principle), Smale — Hirsch      63
Homotopy, holonomic      11
Homotopy, regular      1 34
Homotopy, tangential      37
Immersion      1 34 48
Immersion relation      48
Immersion, $\varepsilon$ -coisotropic      167
Immersion, $\varepsilon$ -isotropic      167
Immersion, $\varepsilon$ -Lagrangian      167
Immersion, A-directed      39
Immersion, co-real      78
Immersion, coisotropic      78
Immersion, complex      78 168
Immersion, contact      87
Immersion, isocomplex      78
Immersion, isocontact      87 138
Immersion, isometric      1 181
Immersion, isosymplectic      78 143
Immersion, isotropic      78 87
Immersion, Lagrangian      78
Immersion, Legendrian      87
Immersion, real      78 168
Immersion, subcritical      87
Immersion, symplectic      78
Isotopy, Hamiltonian      91
Isotopy, Legendrian      91
Kaehler manifold      75
Kaehler metric      75
Liouville structure      90
Manifold, almost complex      75
Manifold, almost Kaehler      75
Manifold, almost symplectic      75
Manifold, complex      75 76
Manifold, contact      82
Manifold, Hermitian      75
Manifold, Kaehler      75
Manifold, open      35
Manifold, symplectic      75 76
Map, fibered      58
Map, free      3
Map, short      181
Map, strictly short      181
Map, transversal to a distribution      65
Map, transversal to a stratified set      14
Map, transversal to a submanifold      13
Microextension trick      63
Monomorphism      37
Monomorphism, contact      87
Monomorphism, isocontact      87 139
Monomorphism, isosymplectic      106 143
Monomorphism, symplectic      106
Nash — Kuiper theorem      182
Nijenhuis tensor      75
Operator, formally invertible      172
Operator, pure differential      172
Petals      150
Polyhedra      14
Positivity condition      101
Primitive quadratic form      183
Primitive semi-Riemannian metric      183
Principal direction      162
Principal subspace      162
Product of paths, uniform      152
Product of paths, weighted      152
Projectivization      86
r-jet      8 9
r-jet extension      8 10
Reeb foliation      84
Reeb vector field      84
Removal of singularities      XII
Riemannian -manifolds      181
Riemannian -metric      181
Section      7
Section, $\Sigma$ -non-singular      49
Section, fiberwise holonomic      22
Section, holonomic      11
Section, transversal to a distribution      65
Semi-Riemannian metric      181
Set, ample      148
Set, m-complete      41
Set, stratified      14
Short formal solution      149
Short path      147
Singularity      49
Singularity, thin      163
Singularity, thin in the coordinate directions      160
Smale's sphere eversion      34
Solution      50 51
Solution, formal      XI 50 51
Solution, genuine      50
Solution, r-extended      50
Space of complex structures      72
Space of r-jets      8
Space of symplectic structures      70
Stability theorems      80 88
Standard contact structure on $\mathbb R^{2n-1}$       82

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