Linear Wavefronts of Convex Polyhedra
- Autores: Makeev V.1, Makeev I.2
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Afiliações:
- St.Petersburg State University
- SPbGU ITMO
- Edição: Volume 212, Nº 5 (2016)
- Páginas: 550-551
- Seção: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237069
- DOI: https://doi.org/10.1007/s10958-016-2686-4
- ID: 237069
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Resumo
Let M ⊂ ℝn be a convex polyhedron, i.e., the intersection of a finite number of closed half-spaces that is bounded and has nonempty interior. Let each hyperplane of the hyperfaces f1, . . . , fm of M move inwards M in a self-parallel fashion at a constant nonnegative speed (it is assumed that at least one face has nonzero speed). This yields a “shrinking” polyhedron. Let reg(f1), . . . , reg(fm) be the parts of M (with disjoint interiors) swept by the faces f1, . . . , fm during the “shrinking” process. The main result is as follows. Let F be a functional on the class of convex compact subsets in ℝn. It is assumed that F is nonnegative and continuous (with respect to the Hausdorff metric) and, furthermore, F(K) = 0 if and only if dim(K) < n. Then for each m-tuple (x1, . . . , xm) of nonnegative reals with nonzero sum there exists an m-tuple of “velocities” for the faces f1, . . . , fm such that the m-tuple (F(reg(f1)), . . . , F(reg(fm))) is proportional to (x1, . . . , xm). Bibliography: 1 title.
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Sobre autores
V. Makeev
St.Petersburg State University
Autor responsável pela correspondência
Email: mvv57@inbox.ru
Rússia, St.Petersburg
I. Makeev
SPbGU ITMO
Email: mvv57@inbox.ru
Rússia, St.Petersburg