A. D. Alexandrov Selected Works: Selected Scientific Papers

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Yu. G. Reshetnyak, S.S. Kutateladze
CRC Press, Feb 21, 2002 - Mathematics - 332 pages
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Alexandr Danilovich Alexandrov has been called a giant of 20th-century mathematics. This volume contains some of the most important papers by this renowned geometer and hence, some of his most influential ideas. Alexandrov addressed a wide range of modern mathematical problems, and he did so with intelligence and elegance, solving some of the discipline's most difficult and enduring challenges. He was the first to apply many of the tools and methods of the theory of real functions and functional analysis that are now current in geometry. The topics here include convex polyhedrons and closed surfaces, an elementary proof and extension of Minkowski's theorem, Riemannian geometry and a method for Dirichlet problems. This monograph, published in English for the first time, gives unparalleled access to a brilliant mind, and advanced students and researchers in applied mathematics and geometry will find it indispensable.
 

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Contents

An elementary proof of the Minkowski and some
19
To the theory of mixed volumes of convex bodies
31
To the theory of mixed volumes of convex bodies
99
To the theory of mixed volumes of convex bodies
119
A general uniqueness theorem for closed surfaces
145
On the area function of a convex body
155
Intrinsic geometry of an arbitrary convex surface
163
Existence of a convex polyhedron and a convex
169
On tiling a space with polyhedra
175
On a generalization of Riemannian geometry
187
The Dirichlet problem for the equation
251
A general method for dominating solutions
273
On the principles of relativity theory
289
Index
319
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