  We study the problem of removable singularities for degenerate elliptic
equations. Let F be a fully nonlinear second-order partial differential
subequation of degenerate elliptic type on a manifold X. We study the question:
Which closed subsets E in X have the property that every F-subharmonic function
(subsolution) on X-E, which is locally bounded across E, extends to an
F-subharmonic function on X. We also study the related question for F-harmonic
functions (solutions) which are continuous across E. Main results assert that
if there exists a convex cone subequation M such that F+M is contained in F,
then any closed set E which is M-polar has these properties. To be M-polar
means that E = {f = -\infty} where f is M-subharmonic on X and smooth outside
of E. Many examples and generalizations are given. These include removable
singularity results for all branches of the complex and quaternionic
Monge-Ampere equations, and a general removable singularity result for the
harmonics of geometrically defined subequations.
  For pure second-order subequations in R^n with monotonicity cone M, the Riesz
characteristic p = p(M) is introduced, and extension theorems are proved for
any closed singular set E of locally finite Hausdorff (p-2)-measure (or, more
generally, of (p-2)-capacity zero). This applies for example to branches of the
equation s_k(D^2 u) = 0 (kth elementary function) where p(M) = n/k.
  For convex cone subequations themselves, several removable singularity
theorems are proved, independent of the results above.
