Geodesic Distance Riesz Energy on Projective Spaces
| Autor: | Bilyk, Dmitriy, Matzke, Ryan W., Nathe, Joel |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We study probability measures that minimize the Riesz energy with respect to the geodesic distance $\vartheta (x,y)$ on projective spaces $\mathbb{FP}^d$ (such energies arise from the 1959 conjecture of Fejes T\'oth about sums of non-obtuse angles), i.e. the integral \begin{equation} \frac{1}{s} \int_{\mathbb{FP}^d} \int_{\mathbb{FP}^d} \big( \vartheta (x,y) \big)^{-s} d\mu(x) d\mu (y) \,\,\, \text{ for } \,\,\, s |
| Databáze: | arXiv |
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