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arXiv · 2210.06727

Sharp Stability of Log-Sobolev and Moser-Onofri inequalities on the Sphere

Lu Chen·Guozhen Lu·Hanli Tang
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Abstract

In this paper, we are concerned with the stability problem for endpoint conformally invariant cases of the Sobolev inequality on the sphere $\mathbb{S}^n$. Namely, we will establish the stability for Beckner's log-Sobolev inequality and Beckner's Moser-Onofri inequality on the sphere. We also prove that the sharp constant of global stability for the log-Sobolev inequality on the sphere $\mathbb{S}^n$ must be strictly smaller than the sharp constant of local stability for the same inequality. Furthermore, we also derive the non-existence of the global stability for Moser-Onofri inequality on the sphere $\mathbb{S}^n$.

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Lu Chen, Guozhen Lu, Hanli Tang. 2022-10-13. Sharp Stability of Log-Sobolev and Moser-Onofri inequalities on the Sphere. https://arxiv.org/abs/2210.06727

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