Complex Analysis - Several Complex Variables and Connections - download pdf or read online

By Peter Ebenfelt, Norbert Hungerbühler, Joseph J. Kohn, Ngaiming Mok, Emil J. Straube

ISBN-10: 3034600089

ISBN-13: 9783034600088

This quantity represents the complaints of a convention on a number of complicated Variables, PDE's, geometry, and their interactions, held July 7-11, 2008 on the college of Fribourg, Switzerland, in honor of Linda Rothschild. The participants are top specialists who have been invited plenary audio system on the convention, or who have been invited by means of the editors to give a contribution to this quantity.

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Additional resources for Complex Analysis - Several Complex Variables and Connections with PDE Theory, and Geometry

Example text

When S ∗ is not connected, it is possible that both apply, because it may exist at ˜ n−1 (u) inducing γ˜ on S˜ı∗ which the same time a global section on S˜∗ of the sheaf H is extendable at the origin, and another one which is not extendable at the origin. 2. 1, assume that we have a global ˜ on S˜∗ of the local system H ˜ n−1 (u) inducing γ˜ on S˜ı∗ which is not section W extendable at the origin. Then there exists Ω ∈ Γ(X, ΩnX ) and l ∈ [1, k] with the following properties: df l dt (1) dΩ = (m + u) ∧Ω+ ∧ Ω; f k t (2) along S ∗ the n-meromorphic (δu − lk dt ∧)-closed form Ω/f m induces t τˇ1 (σ) = df ∧ σ in the sheaf hn (Γl ), for some global section σ on S ∗ of f n−1 (Γl ); the sheaf h (3) the current on X of type (n + 1, 0) with support {0} : P2 λ = −m − u, P f μ = −(k − l )/k, defines a non zero class in X n+1 H[0] (X, OX ) |f |2λ f¯m−j |t|2μ df ∧Ω∧ f for j large enough in N.

2. Let Σ be a real analytic involutive system of first-order partial differential equations of rank n on a real analytic manifold M. Let W + and W − be real analytic wedges in M with a real analytic edge E having opposite directions at p ∈ E, that is Γp (W + ) = −Γp (W − ). Let u+ ∈ C 2 (W + ), u− ∈ C 2 (W − ) be solutions in W + and W − respectively such that u+ |E = u0 = u− |E , and assume that + − CTp M = CTp E ⊕ Vp (where Vp = Vpu = Vpu ). Then, W Fa (u0 )|p ⊆ ι∗E (Tp◦ (M)). Proof. 1 we know that W Fa (u0 ) ⊆ (ΓTp (W + ))◦ ∩ (ΓTp (W − ))◦ .

2 that is, not inducing 0 in the Milnor fibre of f˜ at 0 Oblique Polar Lines of [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] X |f |2λ |g|2μ 23 , Sur certaines singularit´es d’hypersurfaces II, J. Algebraic Geometry 17 (2008), 199–254. D. -M. Maire, D´eveloppements asymptotiques, transformation de Mellin complexe et int´egration sur les fibres, Springer Lecture Notes 1295, Springer, 1987, pp. 11–23. , Asymptotic expansion of complex integrals via Mellin transform, J. Funct. Analysis 83 (1989), 233–257.

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Complex Analysis - Several Complex Variables and Connections with PDE Theory, and Geometry by Peter Ebenfelt, Norbert Hungerbühler, Joseph J. Kohn, Ngaiming Mok, Emil J. Straube


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