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<p>In 1988, W. Kuperberg conjectured that small enough packing density implies large enough covering density and vice versa. Recently, Prosanov proved the translative case of this conjecture. In this paper, we present a proof for Kuperberg’s conjecture in the case of bounded roundness.</p>

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On a Conjecture of W. Kuperberg

  • 期刊论文

  • 发表日期：

    2025年3月15日

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  • Shiyun Wen

摘要

In 1988, W. Kuperberg conjectured that small enough packing density implies large enough covering density and vice versa. Recently, Prosanov proved the translative case of this conjecture. In this paper, we present a proof for Kuperberg’s conjecture in the case of bounded roundness.