First, understand Science and Technology is Not Magic. It has limitations. 11 billion is way to many people for a land of abundance, that you speak of. Survive? at what price? Our technology is still primitive and frail.

We can orbit a tin can around the Earth, Take a few steps on the moon, and operate a toy RC Model Car on Mars. But that is a far cry from mass exploitation of resources in Space. The cost and the amount of energy to do it, would be prohibitive. Look at how much our current space program is suffering due to budget costs.

The Human Mind has limitations, just as any animal has. It is not Magic. Technology we have is very frail. Subject to natural and human forces. When our world dies, we will die with it. It is just that simple.