Growth of balls in the universal cover of surfaces and graphs
Growth of balls in the universal cover of surfaces and graphs
In this paper, we prove uniform lower bounds on the volume growth of balls in the universal covers of Riemannian surfaces and graphs. More precisely, there exists a constant $\delta >0$ such that if $(M,hyp)$ is a closed hyperbolic surface and $h$ another metric on $M$ with $\mathrm {Area}(M,h)\leq \delta …