In Infinite Volume but Finite Surface Area a question is asked whether there is some shape in $\Bbb R^3$ that have an infinite volume, but a finite surface area, sort of the opposite of Gabriel's Horn.
The answer seems to be that there is none, if there is a surface area. (which seems reasonable). Would that still hold if we extend to $\Bbb R^n$ (volume defined as $n$ dimensions, area $n-1$ dimensions)? Any other mathematical room where it would be possible?
Not sure what I should tag this question with