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We consider the standard first passage percolation model on Z^d with adistribution G on R+ that admits an exponential moment. We study the maximalflow between a compact convex subset A of R^d and infinity. The study ofmaximal flow is associated with the study of sets of edges of minimal capacitythat cut A from infinity. We prove that the rescaled maximal flow between nAand infinity $\phi$(nA)/n^ (d--1) almost surely converges towards adeterministic constant depending on A. This constant corresponds to thecapacity of the boundary $\partial$A of A and is the integral of adeterministic function over $\partial$A. This result was shown in dimension 2and conjectured for higher dimensions by Garet in [6].

The maximal flow from a compact convex subset to infinity in first passage percolation on Z^d