The paper defines the mth order p-affine capacity, proves its fundamental properties and exact unit ball value, and establishes affine isocapacity inequalities relating it to volume, p-capacity, mth order integral affine surface area, and L_p surface area.
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On the $m$th order $p$-affine capacity
The paper defines the mth order p-affine capacity, proves its fundamental properties and exact unit ball value, and establishes affine isocapacity inequalities relating it to volume, p-capacity, mth order integral affine surface area, and L_p surface area.