Geometria Complessa e Geometria Differenziale
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D. Angella - S. Calamai

A vanishing result for strictly p-convex domains

created by daniele on 08 Nov 2016
modified on 17 Nov 2017


Published Paper

Inserted: 8 nov 2016
Last Updated: 17 nov 2017

Journal: Ann. Mat. Pura Appl.
Volume: 193
Number: 4
Pages: 1069-1084
Year: 2014
Doi: 10.1007/s10231-012-0315-5

ArXiv: 1211.2564 PDF
Links: arXiv:1211.2564


In view of A. Andreotti and H. Grauert's vanishing theorem for q-complete domains in Cn, (Th\'eor\`eme de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France 90 (1962), 193--259,) we re-prove a vanishing result by J.-P. Sha, (p-convex Riemannian manifolds, Invent. Math. 83 (1986), no. 3, 437--447,) and H. Wu, (Manifolds of partially positive curvature, Indiana Univ. Math. J. 36 (1987), no. 3, 525--548,) for the de Rham cohomology of strictly p-convex domains in Rn in the sense of F. R. Harvey and H. B. 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 L. H\"ormander, (An introduction to complex analysis in several variables, Third edition, North-Holland Mathematical Library, 7, North-Holland Publishing Co., Amsterdam, 1990,) and A. Andreotti and E. Vesentini, (Carleman estimates for the Laplace-Beltrami equation on complex manifolds, Inst. Hautes \'Etudes Sci. Publ. Math. 25 (1965), 81--130).

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