논문KCI 등재
Stability of the dibar-estimates and the Mergelyan property for weakly q-convex manifolds
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Let r >= q. We get the stability of the estimates of the dibar-Neumann problem for (p; r)-forms on a weakly q-convex complex submanifold. As a by-product of the stability of the divar-estimates, we get the Mergelyan approximation property for (p; r)-forms on a weakly q-convex complex submanifold which satisfies property (P).
Abstract
Let r >= q. We get the stability of the estimates of the dibar-Neumann problem for (p; r)-forms on a weakly q-convex complex submanifold. As a by-product of the stability of the divar-estimates, we get the Mergelyan approximation property for (p; r)-forms on a weakly q-convex complex submanifold which satisfies property (P).
참고문헌 (9)
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- H. R. Cho, "of the estimates for @-equation on compact pseudoconvex complex manifolds", Kyushu J. Math, 48(1), pp.29~34 (1994)
- H. R. Cho, "Holomorphic approximation on compact pseudoconvex complex manifolds", The Journal of Geometric Analysis, 8(3), pp.427~432 (1998)
- L.-H. Ho, "@-problem on weakly q-convex domains", Math. Ann, 290, pp.3~18 (1991)
- L. Hormander, "L2 estimates and existence theorem for the @ operator", Acta Math, 113, pp.89~ (1965)[DOI]
- L. Hormander, "An introduction to complex analysis in several variables" (1979), North-Holland
- J. J. Kohn, "Global regularity for @ on weakly pseudoconvex manifolds", Trans. Amer. Math. Soc, 181, pp.273~292 (1973)
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