2 problems

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Holevo–Utkin conjecture on sharp $\ell_p$ norms for zero-sum vectors
Holevo–Utkin conjecture. For $0<p\le 1$ ,
Conjectureopenfunctional-analysis lp-norms zero-sum-vectorsarXiv posted 2 days ago
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Asymptotic $L^p$ symmetry conjecture for positive and negative parts of eigenfunctions
Let $(M,g)$ be a given Riemannian manifold, let $\psi_{\lambda}$ be a real Laplace eigenfunction, and let $1<p<\infty$ . For a set $A\subseteq M$ , write $\chi_A$ for its characteris…
Problemopenlaplace-eigenfunctions lp-norms spectral-geometryarXiv posted 2 days ago

Holevo–Utkin conjecture on sharp ℓp\ell_pℓp​ norms for zero-sum vectors