Reconstruction of Crofton Measures from Projective Finsler Metrics in R3
Rafik Aramyan
TL;DR
This paper develops an integral geometry-based method to reconstruct Crofton measures from projective smooth Finsler metrics in three-dimensional space, addressing a classical problem in integral geometry.
Contribution
It introduces an inversion formula for reconstructing Crofton measures from projective Finsler metrics in R3, advancing the solution of Hilbert's fourth problem.
Findings
Derived an explicit inversion formula
Reconstructed Crofton measures from Finsler metrics
Enhanced understanding of integral geometry in R3
Abstract
A solution of Hilberts fourth problem lead to integral equation of the type generalized cosine transform. The present paper considers the solution that integral equation by integral geometry methods and propose an inversion formula for reconstruction of Crofton measures from projective smooth Finsler metrics in R3.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Differential Geometry Research · Cosmology and Gravitation Theories · Relativity and Gravitational Theory