Isolated singularities for some types of curvature equations

AbstractWe consider the removability of isolated singularities for the curvature equations of the form Hk[u]=0, which is determined by the kth elementary symmetric function, in an n-dimensional domain. We prove that, for 1⩽k⩽n−1, isolated singularities of any viscosity solutions to the curvature equations are always removable, provided the solution can be extended continuously at the singularities. We also consider the class of “generalized solutions” and prove the removability of isolated singularities