Consider the L1-ball $A$ and the L2-ball $B$ in $d$-dimensions. Consider the Minkowski sum $A+B$ of the two corresponding sets of points. Is there a known expression for the Vol$(A+B)$ or the surface area of $A+B$? Or, is there some interesting upper-bound on the quantities?
2026-03-28 11:37:23.1774697843
Surface area of L2 ball + L1 ball
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You can exemplify by 3 dimensional case. The volume is sum of following terms
volume of A itself
for every face of A, product of area of face and radius of B
for every edge of A, product of length of edge and area of 1/4 circle with radius of B
for every vertex of A, volume of 1/8 sphere
So for dimension $n$, each $i$-face contributes product of volume of that surface multiplies volume of positive quadrant of unit ball in $\mathbb{R}^{n-i}$. And surface area are derivative of volume w.r.t radius of B