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
Previous Page Next Page