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In mathematics, the Besicovitch inequality … In mathematics, the Besicovitch inequality is a geometric inequality relating volume of a set and distances between certain subsets of its boundary. The inequality was first formulated by Abram Besicovitch. Consider the n-dimensional cube with a Riemannian metric . Let denote the distance between opposite faces of the cube. The Besicovitch inequality asserts that The inequality can be generalized in the following way. Given an n-dimensional Riemannian manifold M with connected boundary and a smooth map , such that the restriction of f to the boundary of M is a degree 1 map onto , define Then . The Besicovitch inequality was used to prove systolic inequalitieson surfaces.to prove systolic inequalitieson surfaces.
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| rdfs:comment |
In mathematics, the Besicovitch inequality … In mathematics, the Besicovitch inequality is a geometric inequality relating volume of a set and distances between certain subsets of its boundary. The inequality was first formulated by Abram Besicovitch. Consider the n-dimensional cube with a Riemannian metric . Let denote the distance between opposite faces of the cube. The Besicovitch inequality asserts that The inequality can be generalized in the following way. Given an n-dimensional Riemannian manifold M with connected boundary and a smooth map , such that the restriction of f to the boundary of M is a degree 1 map onto , define Then .f M is a degree 1 map onto , define Then .
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| rdfs:label |
Besicovitch inequality
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