Displaying similar documents to “Minimal equations, global reducibility of holomorphic functions, and relative rationality of analytic sets”

On envelopes of holomorphy of domains covered by Levi-flat hats and the reflection principle

Joël Merker (2002)

Annales de l’institut Fourier

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In the present paper, we associate the techniques of the Lewy-Pinchuk reflection principle with the Behnke-Sommer continuity principle. Extending a so-called to a parameterized congruence of Segre varieties, we are led to studying the envelope of holomorphy of a certain domain covered by a smooth Levi-flat “hat”. In our main theorem, we show that every 𝒞 ∞ -smooth CR diffeomorphism h : M → M ' between two globally minimal real analytic hypersurfaces in ℂ n ( n ≥ 2 ) is real analytic at every point of M ...

The index of a vector field tangent to a hypersurface and the signature of the relative jacobian determinant

Xavier Gómez-Mont, Pavao Mardešić (1997)

Annales de l'institut Fourier

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Given a real analytic vector field tangent to a hypersurface V with an algebraically isolated singularity we introduce a relative Jacobian determinant in the finite dimensional algebra B Ann B ( h ) associated with the singularity of the vector field on V . We show that the relative Jacobian generates a 1-dimensional non-zero minimal ideal. With its help we introduce a non-degenerate bilinear pairing, and its signature measures the size of this point with sign. The signature satisfies a law of conservation...