Before revision:  This is lower than her Maxmin utility : that of her worst share in the best possible partition. When the manna is unanimously good, or unanimously bad, better guarantees than minMax are feasible.
After revision:  This is lower than her Maxmin utility : that of her worst share in the best possible n-partition. The Maxmin guarantee is not feasible, even with two agents, if non convex preferences are allowed. The minMax guarantee is feasible in the very general class of problems where the manna is non atomic and utilities are continuous, but not necessarily additive or monotonic. The proof uses advanced algebraic topology techniques. And the minMax guarantee is implemented by the n-person version of Divide and Choose due to Kuhn (1967). When utilities are co-monotone (a larger part of the manna is weakly better for everyone, or weakly worse for everyone) better guarantees than minMax are feasible.