Singularities and the wave equation on conic spaces

TL;DR

This paper studies how singularities in solutions to the wave equation behave on manifolds with conic singularities, revealing a mixture of diffraction and geometric propagation at cone points.

Contribution

It provides a detailed analysis of wave singularity propagation on conic spaces, combining diffractive and geometric effects.

Findings

Singularities diffract and propagate geometrically at cone points.

Wave solutions exhibit mixed behavior due to conic singularities.

Analysis advances understanding of wave behavior on singular spaces.

Abstract

Let $X$ be a manifold with boundary, endowed with a metric with conic singularities at the boundary components of $X$. Let $u$ be a solution to the wave equation on $\mathbb{R} \times X$. When a singularity of $u$ strikes a cone point of $X$, it undergoes a mixture of diffractive spreading and geometric propagation.