A vanishing result for strictly $$p$$ -convex domains

Angella, Daniele and Calamai, Simone (2012) A vanishing result for strictly $$p$$ -convex domains. Annali di Matematica Pura ed Applicata . ISSN 0373-3114 (In Press)

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Abstract

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).

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