LELONG NUMBERS OF m-SUBHARMONIC FUNCTIONS ALONG SUBMANIFOLDS

Abstract

Abstract We study the possible singularities of an m-subharmonic function $\varphi $ along a complex submanifold V of a compact Kähler manifold, finding a maximal rate of growth for $\varphi $ which depends only on m and k, the codimension of V. When $k < m$ , we show that $\varphi $ 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.