As of right now, the average Chinese person emits as much carbon as the average European [todayonline.com] -- and there are many more Chinese people.
Most of the Chinese emissions are for the creation of products shipped to Europe and the US. These are basically emissions that are exported to China.
At some point, we will have used up enough land so that pollution, species loss and loss of renewable resources makes us get a Darwin award as a species.
Species grow until they reach the carrying capacity of the environment. They don't die out when they do, they stabilize and/or evolve. Humans have done this many times before.