3 problems

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Nonexistence of self-extremal sets in $\ell_p$ for $1<p<2$
Nonexistence conjecture. There are no self-extremal sets in $\ell_p$ for $1<p<2$ .
Conjectureopenbanach-spaces ell-p-spaces extremal-setsarXiv posted 2 days ago
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The numerical-index conjecture for two-dimensional real \ell_p spaces
Let $\ell_p^2$ be the two-dimensional real $\ell_p$ space, let $n(\ell_p^2)$ denote its numerical index, and let … be the rotation by $90^\circ$ . The numerical-index conjecture. Th…
Conjectureopenbanach-spaces ell-p-spaces numerical-indexarXiv posted 2 days ago
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Optimality conjecture for geometric spanners in finite \ell_p metrics
For $1<p\leq 2$ , consider geometric spanners for finite subsets of $\ell_p$ with stretch $t$ . Geometric spanner optimality conjecture. Tight instances exist in these spaces; that i…
Conjectureopenell-p-spaces geometric-spanners metric-geometryarXiv posted 2 days ago

Nonexistence of self-extremal sets in ℓp\ell_pℓp​ for 1<p<21<p<21<p<2