Regularity in the Local CR Embedding Problem |
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Authors: | Xianghong Gong S M Webster |
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Institution: | 1.Department of Mathematics,University of Wisconsin,Madison,USA;2.Department of Mathematics,University of Chicago,Chicago,USA |
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Abstract: | We consider a formally integrable, strictly pseudoconvex CR manifold M of hypersurface type, of dimension 2n?1≥7. Local CR, i.e., holomorphic, embeddings of M are known to exist from the works of Kuranishi and Akahori. We address the problem of regularity of the embedding in standard Hölder spaces C a (M), a∈R. If the structure of M is of class C m , m∈Z, 4≤m≤∞, we construct a local CR embedding near each point of M. This embedding is of class C a , for every a, 0≤a<m+(1/2). Our method is based on Henkin’s local homotopy formula for the embedded case, some very precise estimates for the solution operators in it, and a substantial modification of a previous Nash–Moser argument due to the second author. |
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