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We study the space of Hopf differentials of almost fuchsian minimalimmersions of compact Riemann surfaces. We show that the extrinsic curvature ofthe immersion at any given point is a concave function of the Hopfdifferential. As a consequence, we show that the set of all such Hopfdifferentials is a convex subset of the space of holomorphic quadraticdifferentials of the surface. In addition, we address the non-equivariant case,and obtain lower and upper bounds for the size of this set.

On a convexity property of the space of almost fuchsian immersions