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Let (M,θ) be a compact CR manifold of dimension 2n+1 with a contact form θ, and L=(2+2/n)Δ
+R its associated CR conformal laplacien. The CR Yamabe conjecture states that there is a contact form &θtilde; on M conformal to θ which has a constant Webster curvature. This problem is equivalent to...
We study some problems of optimal distribution of masses, and we show that they can be characterized by a suitable Monge-Kantorovich equation. In the case of scalar state functions, we show the equivalence with a mass transport problem, emphasizing its geometrical approach through geodesics. The...
We perform descent calculations for the families of elliptic curves over Q with a rational point of order n = 5 or 7. These calculations give an estimate for the Mordell-Weil rank which we relate to the parity conjecture. We exhibit explicit elements of the Tate-Shafarevich group of order 5 and...
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