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Mixed Volumes. Minkowski Problem. Selected Global Problems in Geometric Partial Differential Equations

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Abstract

Let Vn+1 be a (n + 1)-dimensional Euclidean vector space. We denote by En+1 the (n + 1)-dimensional Euclidean point space associated with Vn+1 (see §1). Then every vector aVn+1 generates a parallel translation

$$ {p_{a}}:{E^{{n + 1}}} \to {E^{{n + 1}}}$$
(7.1)

in the following way: for any point XEn+1

$$ {p_{a}}\left( X \right) = X', $$

, where X’ is the terminal point of the vector \( \overline {XX'} = a \).

Keywords

  • Convex Body
  • Gaussian Curvature
  • Global Problem
  • Convex Polyhedron
  • Parallel Translation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1994 Springer-Verlag Berlin Heidelberg

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Bakelman, I.J. (1994). Mixed Volumes. Minkowski Problem. Selected Global Problems in Geometric Partial Differential Equations. In: Convex Analysis and Nonlinear Geometric Elliptic Equations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69881-1_2

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  • DOI: https://doi.org/10.1007/978-3-642-69881-1_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-69883-5

  • Online ISBN: 978-3-642-69881-1

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