The Euler characteristic of a surface from its Fourier analysis in one direction
Geometric Topology
2014-09-15 v2 Analysis of PDEs
Abstract
In this paper, we prove that we can recover the genus of a closed compact surface in from the restriction to a generic line of the Fourier transform of the canonical measure carried by . We also show that the restriction on some line in Minkowski space of the solution of a linear wave equation whose Cauchy data comes from the canonical measure carried by , allows to recover the Euler characteristic of .
Keywords
Cite
@article{arxiv.1408.1115,
title = {The Euler characteristic of a surface from its Fourier analysis in one direction},
author = {Nguyen Viet Dang},
journal= {arXiv preprint arXiv:1408.1115},
year = {2014}
}
Comments
Section 3 entirely rewritten, appendix made shorter, formula (8) in Theorem 2.1 for $\chi(S)$ in the older version had wrong sign now corrected, new results related to the Radon transform added