Lagrangian distributions on asymptotically Euclidean manifolds

TL;DR

This paper introduces Lagrangian distributions on scattering manifolds, extending the concept to manifolds with corners and scattering symplectic structures, and studies their principal symbols.

Contribution

It develops the theory of Lagrangian distributions on scattering manifolds, including the definition and analysis of their principal symbols, a novel extension in geometric analysis.

Findings

Defined Lagrangian distributions on scattering manifolds

Analyzed the principal symbol of these distributions

Extended classical theory to manifolds with corners

Abstract

We develop the notion of Lagrangian distribution on scattering manifolds, meaning on the compactified cotangent bundle, which is a manifold with corners equipped with a scattering symplectic structure. In particular, we study the notion of principal symbol of the arising class of distributions.