在hq上。二阶卡诺群上的李不等式

Pub Date : 2023-10-24 DOI:10.5802/crmath.475

Ye Zhang

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引用次数: 0

摘要

在这篇笔记中，我们证明了热半群的梯度估计，或者更准确地说是h - q。李不等式，在张张化、一些合适的群上胚、中心和条件下保持。我们还建立了h - q对应的黎曼方程。李不平等。作为副产品，我们提供了一个更简单的证明，证明h - q中的常数。李不等式严格大于1。

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On the H.-Q. Li inequality on step-two Carnot groups

In this note we show that the gradient estimate of the heat semigroup, or more precisely the H.-Q. Li inequality, is preserved under tensorization, some suitable group epimorphism, and central sum. We also establish the Riemannian counterpart of the H.-Q. Li inequality. As a byproduct, we provide a simpler proof of the fact that the constant in H.-Q. Li inequality is strictly larger than 1.

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