Scholarlink

<p>In this work, we give a sufficient condition for a step-two Carnot group to satisfy the quasi Bakry–Émery curvature condition. As an application, we establish the gradient estimate for the heat semigroup on the free step-two Carnot group with three generators <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11118_2025_10222_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">\(N_{3,2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>N</mi> <mrow> <mn>3</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> </math></EquationSource> </InlineEquation>. Moreover, higher order gradient estimates and Riemannian counterparts are also deduced under an extra condition.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On Gradient Estimates of the Heat Semigroups on Step-Two Carnot Groups

  • 期刊论文

  • 发表日期：

    2025年5月8日

查看全文
  • Sheng-Chen Mao,
  • Ye Zhang

摘要

In this work, we give a sufficient condition for a step-two Carnot group to satisfy the quasi Bakry–Émery curvature condition. As an application, we establish the gradient estimate for the heat semigroup on the free step-two Carnot group with three generators \(N_{3,2}\) N 3 , 2 . Moreover, higher order gradient estimates and Riemannian counterparts are also deduced under an extra condition.