  We obtain estimates for the nonlinear variational capacity of annuli in
weighted R^n and in metric spaces. We introduce four different (pointwise)
exponent sets, show that they all play fundamental roles for capacity
estimates, and also demonstrate that whether an end point of an exponent set is
attained or not is important. As a consequence of our estimates we obtain, for
instance, criteria for points to have zero (resp. positive) capacity. Our
discussion holds in rather general metric spaces, including Carnot groups and
many manifolds, but it is just as relevant on weighted R^n. Indeed, to
illustrate the sharpness of our estimates, we give several examples of radially
weighted R^n, which are based on quasiconformality of radial stretchings in
R^n.
