The first eigenvalue of Dirac and Laplace operators on surfaces

Jean-Francois Grosjean, Emmanuel Humbert

Let $(M,g,\sigma )$ be a compact Riemmannian surface equipped with a spin structure $\sigma$. For any metric $\tilde{g}$ on $M$, we denote by $\mu \_1(\tilde{g})$ (resp. $\lambda \_1(\tilde{g})$) the f…