LELONG NUMBERS OF m-SUBHARMONIC FUNCTIONS ALONG SUBMANIFOLDS

We study the possible singularities of an m-subharmonic function phi along a complex submanifold V of a compact Kahler manifold, finding a maximal rate of growth for phi which depends only on m and k, the codimension of V. When k < m, we show that phi has at worst log poles along V, and that the strength of these poles is moreover constant along V. This can be thought of as an analogue of Siu's theorem.