A vanishing result for strictly p-convex domains

作者：Angella Daniele^*; Calamai Simone

来源：Annali di Matematica Pura ed Applicata, 2014, 193(4): 1069-1084.

DOI：10.1007/s10231-012-0315-5

• p-Convexity in the sense of Harvey and Lawson
• de Rham cohomology
• Vanishing theorems

In view of Andreotti and Grauert (Bull Soc Math France 90:193-259, 1962) vanishing theorem for -complete domains in , 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 -convex domains in in the sense of Harvey and Lawson (The foundations of -convexity and -plurisubharmonicity in riemannian geometry. arXiv:1111.3895v1 [math.DG]). Our proof uses the -techniques developed by Hormander (An introduction to complex analysis in several variables, 3rd edn. North-Holland Publishing Co, Amsterdam 1990), and Andreotti and Vesentini (Inst Hautes A parts per thousand tudes Sci Publ Math 25:81-130, 1965).

• 出版日期2014-8