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Abstract <p> We prove that the Holmes–Thompson area of the hypermetric space <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\ell^1_4\)</EquationSource> </InlineEquation> is not totally convex. This means that for some planes in this space, there are no linear projections onto them that minimize the Holmes–Thompson area. </p>

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The Holmes–Thompson Area of \(\ell^1_4\) Is Not Totally Convex

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • I. M. Vasilyev

摘要

Abstract

We prove that the Holmes–Thompson area of the hypermetric space \(\ell^1_4\) is not totally convex. This means that for some planes in this space, there are no linear projections onto them that minimize the Holmes–Thompson area.