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[PENDING] Improved interpolation inequalities on the sphere Jean Dolbeault, Maria J. Esteban, Michal Kowalczyk, Michael Loss

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Figure 1. Generically γ(β) = 0 has two solutions, β ± (p, d). Plot of p 7→ β ± (p, d) with d = 1 (left) and d = 2 (right) on the first row, d = 3 (left) and d = 4 (right) on the second row, and d = 5 (left) and d = 10 (right) on the third row
Figure 2. Plot of the function ϕ β corresponding to Theorem 1.1.
Figure 3. The plot of ξ 7→ 2 (2−p)−γ 2 (2−p)
Figure 4. Plot of ξ 7→ χ (2) k (ξ)/χ (1) k (ξ) for various values of γ and of ξ 7→ χ (3) k (ξ)/χ (1)k (ξ) (bold curve) when d = 2, p = 3/2, k = 1 and α 1 = 3.
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