### Metastability in reversible diffusion processes I: Sharp asymptotics for capacities and exit times

We develop a potential theoretic approach to the problem of metastability for reversible diffusion processes with generators of the form $-\u03f5\Delta +\nabla F(\xb7)\nabla $ on ${\mathbb{R}}^{d}$ or subsets of ${\mathbb{R}}^{d}$, where $F$ is a smooth function with finitely many local minima. In analogy to previous work on discrete Markov chains, we show that metastable exit times from the attractive domains of the minima of $F$ can be related, up to multiplicative errors that tend to one as $\u03f5\downarrow 0$, to the capacities of suitably constructed sets. We show that these capacities...