Index
admissible boundary conditions, 80
Alexandroff, A. D., 165
asymptotic curves, 148
asymptotic quadrangles, 192
Cartan, E., 31
Cauchy-Kowalevski Theorem, 7
characteristic quadrangles, 192
Christoffel symbols, 34
Codazzi equations, 34
Cohn-Vossen Theorem, 145, 165
conjugate isothermal coordinates, 229
convex caps, 153
Courant-Lebesgue Lemma, 231
curvature tensor, 34
Darboux equations, 46, 168
Darboux systems, 230
Efimov, N. V., 224
flat Klein bottle, 38
flat metrics, 37
flat Mobius band, 39
flat torus, 38
free maps, 5
Friedrichs, K. O., 86
fundamental forms
the first fundamental form, 33
the second fundamental form, 33
Fundamental Theorem of Surfaces, 35
Gauss curvature, 35
Gauss equation, 34
Gauss-Bonnet formula, 196
Gauss-Codazzi system, 34
geodesic coordinates, 6, 38
geodesic curvature, 37
geodesic polar coordinates, 195
Greene, R., 31
Gromov, M. L., 31, 248
Gunther, M., 31, 86
Han, Q., 53, 86, 141
Harnack inequality, 236
Hartman, P., 70
Heinz, E., 247
Herglotz integral formula, 147
Hong, J.-X., 53, 141, 224, 247
hyperbolic plane, 39
infinitesimal isometric deformations, 154
infinitesimal rigidity, 154
interpolation inequalities, 63
isometric deformation, 154
isothermal coordinates, 232
Janet, M., 31
Janet system, 6
Janet-Cartan Theorem, 4
Kohn, J. J., 107
Levi, E., 70
Lin, C.-S., 53, 86, 107, 141
Maeda, Y., 86, 141
mean curvature, 35
method of continuity, 167, 246
Minkowski functions, 169, 241
Nakamura, G., 86, 141
Nash Embedding Theorem, 4
Nash, J., 31, 107
Nash-Moser iterations, 96, 130
Nirenberg, L., 107, 165, 188
normal coordinate systems, 71
normal curvatures, 149
osculating spaces, 4
Pogorelov, A. V., 188
Poincare-Bendixson Theorem, 151
positive disks, 225
Poznyak, E. G., 42
projective plane, 39
proper domains, 192
rigidity, 145
259
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