论文标题
关于溶胶的面积增长
On Area Growth in Sol
论文作者
论文摘要
Let Sol be the $3$-dimensional solvable Lie group whose underlying space is $\mathbb{R}^3$ and whose left-invariant Riemannian metric is given by $$e^{-2z} dx^2 + e^{2z} dy^2 + dz^2.$$ Building on previous joint work with Matei Coiculescu, which characterizes the cut locus in Sol, we prove SOL中Radius R的球体最多有$20πe^r $，规定R足够大。该估计值急剧达到10倍
Let Sol be the $3$-dimensional solvable Lie group whose underlying space is $\mathbb{R}^3$ and whose left-invariant Riemannian metric is given by $$e^{-2z} dx^2 + e^{2z} dy^2 + dz^2.$$ Building on previous joint work with Matei Coiculescu, which characterizes the cut locus in Sol, we prove that the sphere of radius r in sol has area at most $20 πe^r$ provided that r is sufficiently large. This estimate is sharp up to a factor of 10
