  We show that uniform lattices in some semi-simple groups (notably complex
ones) admit Anosov surface subgroups. This result has a quantitative version:
we introduce a notion, called $K$-Sullivan maps, which generalizes the notion
of $K$-quasi-circles in hyperbolic geometry, and show in particular that
Sullivan maps are H\"older. Using this notion, we show a quantitative version
of our surface subgroup theorem and in particular that one can obtain
$K$-Sullivan limit maps, as close as one wants to smooth round circles. All
these results use the coarse geometry of "path of triangles" in a certain flag
manifold and we prove an analogue to the Morse Lemma for quasi-geodesics in
that context.
