A vanishing result for strictly p-convex domains

In view of Andreotti and Grauert (Bull Soc Math France 90:193-259, 1962) vanishing theorem for q-complete domains in ℂn, we reprove a vanishing result by Sha (Invent Math 83(3):437-447, 1986), and Wu (Indiana Univ Math J 36(3):525-548, 1987), for the de Rham cohomology of strictly p-convex domains in ℝn in the sense of Harvey and Lawson (The foundations of p-convexity and p-plurisubharmonicity in riemannian geometry. arXiv:1111.3895v1 [math.DG]). Our proof uses the L2-techniques developed by Hörmander (An introduction to complex analysis in several variables, 3rd edn. North-Holland Publishing Co, Amsterdam 1990), and Andreotti and Vesentini (Inst Hautes Études Sci Publ Math 25:81-130, 1965)