You are leaving out China's extensive relationships in Mexico, the Caribbean, and Central and South Americas. Their clearly apparent willingness to develo[ maritime logistica capability, work through the likes of Messrs. Lula & Chavez, as well as fomenting domestic insurrection here (with the complicity of the fifth column in our universities) are routinely overlooked, both strategically and tactcally.
Why wage war with a nuclear armed, billion-plus population of India? Why piss away their largest trading partner in the U.S.? What is to gain for China by carrying their current pro-Osama bluff too far?
World domination, however foolish or illogical it might be, has always had its attractions.
The sheer size of the American economy, nuclear arsenal, chemical arsenal, biological arsenal, and conventional military rules out any rational consideration of global domination.
At best, China can control its region, though the sheer size and might of India's economy, navy, nuclear arsenal, and population brings even that possibility into extreme question.
China has lost its last two ground wars: its invasion of India in the 1960's and its invasion of North Vietnam in 1979.
In contrast, China has had some serious success growing its economy and peacefully trading with the world.
Going to war with either Taiwan or India will risk nuclear retaliation (even without the U.S.) against Beijing and the Three Gorges Dam...as well as the obliteration of China's entire economy due to all of its manufacturing being on the coast where it can't protect its own infrastructure from counter-attacks.
Thus, China lives in a region of powers such as Japan and India that it may very well never come to dominate. And if China can't dominate its own home region against its local regional rivals, then it is in no position to even *think* about global domination.
It would be lucky to get its 18 nuclear ICBM's past America's new national missile defense shield...and even the mere attempt would end the lives of 1.4 billion Chinese in retaliation.