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arXiv · 2111.03961

The complex plank problem, revisited

Oscar Ortega-Moreno
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Abstract

Ball's complex plank theorem states that if $v_1,\dots,v_n$ are unit vectors in $\mathbb{C}^d$, and $t_1,\dots,t_n$, non-negative numbers satisfying $\sum_{k=1}^nt_k^2 = 1,$ then there exists a unit vector $v$ in $\mathbb{C}^d$ for which $|\langle v_k,v \rangle | \geq t_k$ for every $k$. Here we present a streamlined version of Ball's original proof.

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Oscar Ortega-Moreno. 2021-11-06. The complex plank problem, revisited. https://arxiv.org/abs/2111.03961

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