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We study the pointwise properties of k-subharmonic functions, that is, the viscosity subsolutions to the fully nonlinear elliptic equations F k [u] = 0, where F k [u] is the elementary symmetric function of order k, 1 ≤ k ≤ n, of the eigenvalues of D 2 u ,Thus 1-subharmonic functions are subharmonic in the classical sense; n-subharmonic functions are convex. We use a special capacity to investigate the typical questions of potential theory: local behaviour, removability of singularities, and polar, negligible, and thin sets, and we obtain estimates for the capacity in terms of the Hausdorff measure. We also prove the Wiener test for the regularity of a boundary point for the Dirichlet problem for the fully nonlinear equation F k [u] = 0. The crucial tool in the proofs of these results is the Radon measure F k [u] introduced recently by N. Trudinger and X.-J. Wang for any k-subharmonic u. We use ideas from the potential theories both for the complex Monge-Ampère and for the p-Laplace equations.

We obtain Serrin type characterization of isolated singularities for solutions of fully nonlinear uniformly elliptic equations F(D 2 u)=0. The main result states that any solution to the equation in the punctured ball bounded from one side is either extendable to the solution in the entire ball or can be controlled near the centre of the ball by means of special fundamental solutions. In comparison with semi-and quasilinear results the proofs use the viscosity notion of generalised solution rather than distributional or Sobolev weak solutions. We also discuss one way of defining

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