  General results on convex bodies are reviewed and used to derive an exact
closed-form parametric formula for the Minkowski sum boundary of $m$ arbitrary
ellipsoids in $N$-dimensional Euclidean space. Expressions for the principal
curvatures of these Minkowski sums are also derived. These results are then
used to obtain upper and lower volume bounds for the Minkowski sum of
ellipsoids in terms of their defining matrices; the lower bounds are sharper
than the Brunn-Minkowski inequality. A reverse isometric inequality for convex
bodies is also given.
