Scholarlink

<p>In this paper, we show that for a Poincaré-Einstein manifold <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((X^{n+1},g_+)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msup> <mi>X</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mo>,</mo> <msub> <mi>g</mi> <mo>+</mo> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> with conformal infinity <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((M,[\hat{g}])\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>M</mi> <mo>,</mo> <mrow> <mo stretchy="false">[</mo> <mover accent="true"> <mi>g</mi> <mo stretchy="false">^</mo> </mover> <mo stretchy="false">]</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> of nonnegative Yamabe type, the fractional Yamabe constants of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\((M,[\hat{g}])\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>M</mi> <mo>,</mo> <mrow> <mo stretchy="false">[</mo> <mover accent="true"> <mi>g</mi> <mo stretchy="false">^</mo> </mover> <mo stretchy="false">]</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> provide lower bounds for the relative volume of geodesic balls in <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\((X, g_+)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <msub> <mi>g</mi> <mo>+</mo> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>.</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

Lower Bounds for the Relative Volume of Poincaré-Einstein Manifolds

  • 期刊论文

  • 发表日期：

    2025年12月5日

查看全文
  • Fang Wang,
  • Huihuang Zhou

摘要

In this paper, we show that for a Poincaré-Einstein manifold \((X^{n+1},g_+)\) ( X n + 1 , g + ) with conformal infinity \((M,[\hat{g}])\) ( M , [ g ^ ] ) of nonnegative Yamabe type, the fractional Yamabe constants of \((M,[\hat{g}])\) ( M , [ g ^ ] ) provide lower bounds for the relative volume of geodesic balls in \((X, g_+)\) ( X , g + ) .