On Area Growth in Sol
Differential Geometry
2021-01-14 v3
Abstract
Let Sol be the -dimensional solvable Lie group whose underlying space is and whose left-invariant Riemannian metric is given by 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 provided that r is sufficiently large. This estimate is sharp up to a factor of 10
Cite
@article{arxiv.2004.10622,
title = {On Area Growth in Sol},
author = {Richard Evan Schwartz},
journal= {arXiv preprint arXiv:2004.10622},
year = {2021}
}
Comments
The previous version of the paper had a bound of $611 e^r$. In this version, I improve the constant from $611$ to $20 \pi$. This is an order of magnitude better. The proof is essentially the same. I am just more careful with the estimates in a few places