I'm not sure why infinite growth wouldn't be possible on a finite planet (even if we assume that "on a finite planet" is indeed a real constraint). Growth doesn't imply greater resource use.
Assuming we need nothing but space to exist in, the surface area of the earth is finite. Expand that by a few km up and down, and humans still have a finite amount of space to live within.
If we're allowed colonization of space, we can only travel at a finite speed. Humans can overtake a finite radius in a year, resulting in a cubic rate of growth in volume. Exponential growth is ultimately limited by the finite speed of light and dimensionality of our universe.
Even if the economy were dominated by the creation and consumption of .mp3 files, an exponentially growing economy would eventually run out of server space and electricity on a finite planet.
If we're allowed colonization of space, we can only travel at a finite speed. Humans can overtake a finite radius in a year, resulting in a cubic rate of growth in volume. Exponential growth is ultimately limited by the finite speed of light and dimensionality of our universe.