Projective convexity in {ie685-1}

Estimates for invariant metrics on $\mathbb C$-convex domains

“…Remark. The same argument implies that G contains the convex hull of any balanced domain lying in G. In particular, the maximal balanced domain lying in G is convex (see also [33]).…”

“…Many of the next proofs will be based on the following geometric property of weakly linearly convex domains (see also [33] and (for the finite type case) [7]).…”

Multi-convex sets in real projective spaces and their duality

“…Remark 3. In a complex projective space, the notion of linearly convex sets has been studied in [12] and [19]. Let us introduce the notion of linearly convex sets in a real projective space P. We first define the following function f from 2 P to 2 P * :…”

“…In a complex projective space, the notion of linearly convex sets has been studied in [12] and [19]. We shall show in Remark 3 that the notion of saturated multi-convex sets is almost identical to that of linearly convex sets defined in a real projective space.…”