arXiv subjects

Pieti Kirkkopelto

Publications and source records attributed to Pieti Kirkkopelto.

3 recordsLinked to original sources

arXiv2026

Classification of singularities of planar slowness surfaces

Slowness surfaces are algebraic varieties arising from propagation of elastic waves. In dimensions $2$, we completely classify the types of singularities slowness surfaces can have. The two types of possible singularities are a transversal self-intersection and a tangential singularity produced by a concentric circle and ellipse that are tangent to each other. To interpret these results analytically, in the case that the slowness surface has transversal self-intersections, we show that the principal symbol of the elastic wave operator is locally smoothly diagonalizable.

math.AG↗

arXiv2026

Regularity for the Geodesic X-Ray Transform in Nonsmooth Geometry

In this article we give regularity results for the geodesic X-ray transform on nonsmooth simple manifolds. As an application, we improve previous injectivity results for the geodesic X-ray transform acting on $L^p$ functions. The results are based on symbol smoothing arguments for the normal operator and mapping properties of pseudodifferential operators with low regularity symbols.

math.DG↗

arXiv2025

Horizontal and Vertical Regularity of Elastic Wave Geometry

The elastic properties of a material are encoded in a stiffness tensor field and the propagation of elastic waves is modeled by the elastic wave equation. We characterize analytic and algebraic properties a general anisotropic stiffness tensor field has to satisfy in order for Finsler-geometric methods to be applicable in studying inverse problems related to imaging with elastic waves.

math.DG↗