  In this paper we develop the p-thinness and the p-fine topology for the
asymptotic behavior of p-superharmonic functions at singular points. We
consider these as extensions of earlier works on superharmonic functions in
dimension 2, on the Riesz and Log potentials in higher dimensions,, and on
p-harmonic functions. It is remarkable that, contrary to the above cases, the
p-thinness for the singular behavior differs from the p-thinness for continuity
by the Wiener criterion for p-superharmonic functions. As applications of
asymptotic estimates of p-superharmonic functions, we also obtain asymptotic
estimates of solutions to a class of fully nonlinear elliptic equations. This
paper grows out of our recent papers on the potential theory in conformal
geometry.
