## View abstract

### Session S38 - Geometric Potential Analysis

Thursday, July 15, 18:25 ~ 18:55 UTC-3

## The doubling property on compact Lie groups

### Laurent Saloff-Coste

#### Cornell University, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak13975fa01cd5e4f06e50b5097378d817').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy13975fa01cd5e4f06e50b5097378d817 = 'lps2' + '&#64;'; addy13975fa01cd5e4f06e50b5097378d817 = addy13975fa01cd5e4f06e50b5097378d817 + 'c&#111;rn&#101;ll' + '&#46;' + '&#101;d&#117;'; var addy_text13975fa01cd5e4f06e50b5097378d817 = 'lps2' + '&#64;' + 'c&#111;rn&#101;ll' + '&#46;' + '&#101;d&#117;';document.getElementById('cloak13975fa01cd5e4f06e50b5097378d817').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy13975fa01cd5e4f06e50b5097378d817 + '\'>'+addy_text13975fa01cd5e4f06e50b5097378d817+'<\/a>';

In dimension $n$, all Riemannian metrics with non-negative Ricci curvature are uniformly doubling. Indeed, on any such manifold, the ratio of the volume of a ball of radius $2r$ divided by the volume of the concentric ball of radius $r$ is bounded by $2^n$. This talk is concerned with the conjecture that, for any compact Lie group $G$, there is a constant $C(G)$ such that any left-invariant metric is doubling with constant almost $C(G)$.

Joint work with Laurent Saloff-Coste, Nathaniel Eldredge (University of Northern Colorado) and Maria Gordina (University of Connecticut).