@Xiane.
An "aeuropean" world culture if seen would and could only be created at the impetus of large-scale global or regional destrution. There will always be important whites in any global process. Most, as in a vast majority, of publicized liberalism, theories of cultural interconnectivity, and most large-scale left-wing concepts were not necessarily created but fundamentalized by upper-class white liberals. Ironically, in fact, most far-left causes espoused by many of the 'racialist' activists come from pasty-white liberal professors and intelligensia. In this forum, for example, nearly all of the farthest-left posters are, in fact, white liberals, or to put it more broadly, white progressives.
The idea of any simple "kill whitey" policy-based reduction of power would lead to a demolishing of infrastructure and basic lack of human capacity not seen since medeival times. Asian technology and industry is rapidly outpacing Europe and the US. However, the Japanese, as an example, very often borrow US/European ideas to supplement their own, duplicate, or build upon from scratch.
The white identity has lost power and definitely large-scale affiliation. The only thing that could truly restore a collective white consciousness would be, as you said, "a Brown world" overtaking whites. And as I have stated previously and sincerely believe, the only way to achieve a multilateral impotence of the white man would be large-scale war.
Thus, the brown planet theory, actualization, or threat broods a hate war, which causes catstrophic destruction, reducing the technology advantage Whites have, in which case the "brown" nations could easily overcome whites.
Interracial mixing, though favoring minorities, will not in my opinion breed out the white man. The time at which white skin becomes a rare commodity would in fact be the time at which Whites would seek and try their hardest to propagate with one another. And if the Christian church, the Communist movement, and many other famous paradigm shifts in society and our world at large occured are any indication, persecution and rarity is the exact recipe to harden a core constituency, gain power, and achieve the "innocent" moniker, the goal of all peoples and nations.