在hq上。二阶卡诺群上的李不等式

IF 0.8 4区数学 Q2 MATHEMATICS

Comptes Rendus Mathematique 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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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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来源期刊

Comptes Rendus Mathematique 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

115

审稿时长

16.6 weeks

期刊介绍： The Comptes Rendus - Mathématique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, … Articles are original notes that briefly describe an important discovery or result. The articles are written in French or English. The journal also publishes review papers, thematic issues and texts reflecting the activity of Académie des sciences in the field of Mathematics.