The Preservation of Convexity by Geodesics in the Space of K\"ahler Potentials on Complex Affine Manifolds
Abstract
On a compact complex affine manifold with a constant coefficient K\"ahler metric ω0, we introduce a concept: (S,ω0)-convexity and show that (S,ω0)-convexity is preserved by geodesics in the space of K\"ahler potentials. This implies that if two potentials are both strictly (S,ω0)-convex, then the metrics along the geodesic connecting them are non-degenerate.
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