Extrinsic Geometry of Convex Surfaces

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American Mathematical Soc., 1973 - 669 pages
 

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Table des matières

Monotypy of closed convex surfaces
167
Monotypy of convex surfaces with boundary Maximum principle
175
Monotypy of unbounded convex surfaces with total curva ture 2i r
182
Monotypy of unbounded convex surfaces with total curvature less than 2
189
INFINITESIMAL BENDINGS OF CONVEX SURFACES
201
Bending fields of general convex surfaces
202
Fundamental Lemma on bending fields of convex surfaces
211
Bending field of a convex surface with prescribed vertical component along the boundary
219

Existence of a closed convex surface with given metric
22
Curves on a convex surface
25
Area of a convex surface
28
Specific curvature of a convex surface
30
Gluing theorem Other existence theorems
33
Convex surfaces in spaces of constant curvature
35
Manifolds of bounded curvature
38
REGULARITY OF CONVEX SURFACES WITH REGULAR METRIC
44
Extrinsic properties of geodesic lines on a convex surface
45
Special resolution of the radiusvector in the neighborhood of an arbitrary initial point
53
Convex surfaces of bounded specific curvature
57
Construction of a convex surface with infinite upper curvature on a given set of points
64
Auxiliary surface and some of its properties
69
Monotypy of convex caps with regular metric
78
Intrinsic estimates for some geometric quantities along the boundary of an analytic cap
83
Estimate for normal curvatures at interior points of a regular convex cap
89
Existence of an analytic convex cap realizing a given analytic metric
95
Regularity of convex surfaces with regular metric
101
Estimates for the derivatives of the solution of a secondorder elliptic partial differential equation
110
MONOTYPY OF CONVEX SURFACES
119
Curves with i g c of bounded variation
120
On convergence of isometric convex surfaces
131
Mixture of isometric surfaces
137
On isometric convex surfaces in canonical position
144
The auxiliary surface Q and its plane sections
153
Special approximation of a bending field of a general convex surface
233
Estimation of certain integrals
239
Proof of the Fundamental Lemma
252
Rigidity of convex surfaces
260
Applications of the rigidity theorems
266
CONVEX SURFACES IN SPACES OF CONSTANT CURVATURE
270
Elliptic space
271
Convex bodies and convex surfaces in elliptic space
282
Mappings of congruent figures
291
Isometric surfaces
300
Infinitesimal bendings of surfaces in elliptic space
308
Monotypy of general convex surfaces in elliptic space
314
Regularity of convex surfaces with regular metric
322
Regularity of convex surfaces with regular metric in a hyper
331
bolic space
344
CONVEX SURFACES IN RIEMANNIAN SPACE
345
CONVEX SURFACES WITH GIVEN SPHERICAL IMAGE
435
GEOMETRIC THEORY OF MONGEAMPERE EQUATIONS
503
Regularity of generalized solutions of strongly elliptic Monge
564
SURFACES OF BOUNDED EXTRINSIC CURVATURE
571
APPENDIX UNSOLVED PROBLEMS
652
BIBLIOGRAPHY
660
SUBJECT INDEX
667
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