From a skyscraper competition, submitted by Mingxuan Dong, Yuchen Xiang, Aiwen Xie, Xu Han of China:
The project proposes a mega hex grid that evolves around the earth circumference at a stratosphere heigh, the principle that support this hypothesis is that it seem to be that in a building the larger the span is, the scale and the unstableness will proportionally increase. But if the span is large enough within the scale of the earth, the unstableness brought by the size decreases inversely. In this case the network of buildings and bridges connected to each other, covering the entire circumference of the earth, will no longer need structural ground support and can be suspended in the air by the effect of the earth gravity. The elevated bridges and buildings that relate the grid can reach any height with out worrying about overturning, earth-quakes, floods and any other natural disasters.Stratosphere Network of Skyscrapers by Carlos Arzate
Antigrav, if possible (unlikely, at least in current physics), might be used as well.