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We introduce and study a sequence of geometric invariants for convex bodies in finite-dimensional spaces, which is in a sense dual to the sequence of mean Minkowski measures of symmetry proposed by the second author. It turns out that the sequence introduced in this paper shares many nice properties with the sequence of mean Minkowski measures, such as the sub-arithmeticity and the upper-additivity...
Measuring how far a convex body $$\mathcal{K }$$ K (of dimension $$n$$ n ) with a base point $${O}\in \,\text{ int }\,\mathcal{K }$$ O ∈ int K is from an inscribed simplex $$\Delta \ni {O}$$ Δ ∋ O in “minimal” position, the interior point $${O}$$ O can display regular or singular behavior. If $${O}$$ O is a regular point then the $$n+1$$...
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