Abstract
We generalize central-charge relations and differential identities of N=2 Special Geometry to N extended supergravity in any dimension 4 \leq D <10, and p-extended objects. We study the extremization of the ADM mass per unit of p-volume of BPS extended objects. Runaway solutions for a ``dilaton'' degree of freedom leading to a vanishing result are interpreted as BPS extremal states having vanishing Bekenstein-Hawking Entropy.
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