摘要

给定一个$\mathrm{<trans\; data-src="n">n个</trans>}$-维度的紧黎曼流形$<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="M">M（M）</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="g">克</trans>}<trans\; data-src=")">)</trans>$在没有边界的情况下，我们考虑非局部方程

哪里${\mathrm{<trans\; data-src="P">P（P）</trans>}}_{\mathrm{<trans\; data-src="g">克</trans>}}^{\mathrm{<trans\; data-src="s">秒</trans>}}$表示带主符号的分数Paneitz运算符${<trans\; data-src="(">(</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="\Delta ">\Delta </trans>}}_{\mathrm{<trans\; data-src="g">克</trans>}}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="s">秒</trans>}}$,$\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src="\in ">\in </trans><trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=")">)</trans>$,$\mathrm{<trans\; data-src="p">第页</trans>}<trans\; data-src="\in ">\in </trans><trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="2">2</trans>}}_{\mathrm{<trans\; data-src="s">秒</trans>}}^{<trans\; data-src="\ast ">\ast </trans>}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=")">)</trans>$具有${\mathrm{<trans\; data-src="2">2</trans>}}_{\mathrm{<trans\; data-src="s">秒</trans>}}^{<trans\; data-src="\ast ">\ast </trans>}<trans\; data-src=":">:</trans><trans\; data-src="=">=</trans>\frac{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="n">n个</trans>}}{\mathrm{<trans\; data-src="n">n个</trans>}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="s">秒</trans>}}$,$\mathrm{<trans\; data-src="n">n个</trans>}<trans\; data-src=">">></trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="s">秒</trans>}$，表示关键Sobolev指数和$\mathrm{<trans\; data-src="𝜀">𝜀</trans>}<trans\; data-src=">">></trans>\mathrm{<trans\; data-src="0">0</trans>}$是一个小实数参数。我们构建了一系列积极的解决方案${\mathrm{<trans\; data-src="u">u个</trans>}}_{\mathrm{<trans\; data-src="𝜀">𝜀</trans>}}$那个集中精力，如$\mathrm{<trans\; data-src="𝜀">𝜀</trans>}<trans\; data-src="\to ">\to </trans>\mathrm{<trans\; data-src="0">0</trans>}$在平均曲率的临界点附近归零$\mathrm{<trans\; data-src="H">小时</trans>}$对于$\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src="<"><</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src="<"><</trans>\frac{\mathrm{<trans\; data-src="1">1</trans>}}{\mathrm{<trans\; data-src="2">2</trans>}}$和附近涉及流形标量曲率的约化函数的临界点$\mathrm{<trans\; data-src="M">M（M）</trans>}$的$\frac{\mathrm{<trans\; data-src="1">1</trans>}}{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="\le ">\le </trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src="<"><</trans>\mathrm{<trans\; data-src="1">1</trans>}$。

关键词

数学学科分类

里程碑

作者