Displaying similar documents to “Geometric proofs of composition theorems for generalized Fourier integral operators.”

Recovering the total singularity of a conormal potential from backscattering data

Mark S. Joshi (1998)

Annales de l'institut Fourier

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The problem of recovering the singularities of a potential from backscattering data is studied. Let Ω be a smooth precompact domain in ℝ n which is convex (or normally accessible). Suppose V i = v + w i with v ∈ C c ∞ ( ℝ n ) and w i conormal to the boundary of Ω and supported inside Ω ‾ then if the backscattering data of V 1 and V 2 are equal up to smoothing, we show that w 1 - w 2 is smooth.

On topologically distinct infinite families of exact Lagrangian fillings

Roman Golovko (2022)

Archivum Mathematicum

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In this note we construct examples of closed connected Legendrian submanifolds in high dimensional contact vector space that admit an arbitrary finite number of topologically distinct infinite families of diffeomorphic, but not Hamiltonian isotopic exact Lagrangian fillings.

Umbilical characteristic number of Lagrangian mappings of 3-dimensional pseudooptical manifolds

Maxim È. Kazarian (1996)

Banach Center Publications

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As shown by V. Vassilyev [V], D 4 ± singularities of arbitrary Lagrangian mappings of three-folds form no integral characteristic class. We show, nevertheless, that in the pseudooptical case the number of D 4 ± singularities counted with proper signs forms an invariant. We give a topological interpretation of this invariant, and its applications. The results of the paper may be considered as a 3-dimensional generalization of the results due to V. I. Arnold [A].