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The following is essentially a partial case for my previous question.

Let $B\subset\mathbb{R}^m$ be the unit ball with respect to a concrete norm on $\mathbb{R}^m$, say $l^p$-norm, $p\in (1,\infty)$. Let $v_1,...,v_n\in \mathbb{R}^m$ be linearly independent.

How to calculate the $n$-dimensional volume of $B\cap span\{v_1,...,v_n\}$?

I need to express this volume through the coordinates of $v_1,...,v_n$, or perhaps through some distances between certain combinations of them. I know that there is extensive literature on related matters, but I hope that this specific question has a specific answer..

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See http://matwbn.icm.edu.pl/ksiazki/sm/sm88/sm8817.pdf and references therein to other papers by same author to see how to calculate these sections.

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  • $\begingroup$ From quick looking at the papers, and also some more recent ones it seems that there are no explicit formulas, only estimates. Is this correct, and the answer to my question is "it is too complicated to get an explicit formula", or am I having a wrong impression? $\endgroup$
    – erz
    Commented Jun 6, 2019 at 9:56

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