Let $\Sigma^2$ be an orientable compact surface of genus $gen(\Sigma)\geq2$, and denote by $\mathcal M(\Sigma)$ the moduli space of hyperbolic metrics on $\Sigma$, i.e., Riemannian metrics of constant ...
I'm confused about some things concerning lengths of geodesics on Riemann surfaces and positive eigenvalues of the Laplacian. Moreover, I'm also interested in the relation between these two. Let $X$ ...
Lower bound on the first eigenvalue of the Laplacian of a Riemann surface with constant negative scalar curvature
A friend in physics asked this question, and I didn't know the answer. Are there lower bounds on the first eigenvalue of the Laplacian of a Riemann surface equipped with a metric of constant negative ...