Geodesic Convexity of Small Neighborhood in the Space of K\"ahler Potentials
Abstract
We show that, given k> 4, 0<J<\1 4,k-4 4\, any point in space of non-degenerate smooth K\"ahler potentials has a small neighborhood with respect to Ck norm, s.t. any two points in this neighborhood can be connected by a geodesic of at least Ck-J regularity.
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