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The coincidence of the real and complex methods of interpolation is investigated. Positive results are established under the presence of geometrical properties which are expressed in terms of vector valued Fourier transforms. The results are applied to complex interpolation of Hp spaces and to the study of geometrical properties of Banach spaces.

A product of Kähler manifolds also carries a Kähler metric. In this short note, we would like to study the product of generalized p-Kähler manifolds, compact or not. The results we get extend the known results (balanced, SKT, sG manifolds), and are optimal in the compact case. Hence we can give new non-trivial examples of generalized p-Kähler manifolds.

Using shadowing techniques we prove that the Hénon map $H_{a,b}(x,y)=(a-x^{2}+by,x)$ admits a transversal homoclinic point for a set of parameters which is not small. For the area and orientation preserving Hénon map (corresponding to b=-1) we prove that a transversal homoclinic point exists for a≥0.265625. Applying a computer-assisted version of our scheme we show that the result holds even for a≥-0.866. This supports an old conjecture due to Devaney and Nitecki dating back to 1979, see [4], claiming that the Hénon map in the case b=-1 admits a transversal homoclinic point for a>-1.

Yamabe soliton is a self-similar solution to the Yamabe flow on manifolds without boundary. In this paper, we define and study the Yamabe soliton with boundary and conformal mean curvature soliton, which are natural generalizations of the Yamabe soliton. We study these solitons from equation point of view. We also study their two-dimensional analog: the Gauss curvature soliton with boundary and geodesic curvature soliton.

On étudie les surfaces à réseau conjugué dans un espace projectif S2n+1, admettant une déformation projective Cn+1.