A lower bound for the logarithmic energy on $\mathbb{S}^2$ and for the Green energy on $\mathbb{S}^n$

preprint2022arXivOpen access

We show an alternative proof of the sharpest known lower bound for the logarithmic energy on the unit sphere $\mathbb{S}^2$ . We then generalize this proof to get new lower bounds for the Green energy on the unit $n$ -sphere $\mathbb{S}^n$ .

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A lower bound for the logarithmic energy on $\mathbb{S}^2$ and for the Green energy on $\mathbb{S}^n$

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A lower bound for the logarithmic energy on S2\mathbb{S}^2S2 and for the Green energy on Sn\mathbb{S}^nSn

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A lower bound for the logarithmic energy on $\mathbb{S}^2$ and for the Green energy on $\mathbb{S}^n$