Mathematical Research Letters

Volume 23 (2016)

Number 5

The Euler characteristic of a surface from its Fourier analysis in one direction

Pages: 1263 – 1279

DOI: http://dx.doi.org/10.4310/MRL.2016.v23.n5.a2

Author

Nguyen Viet Dang (Laboratoire Paul Painlevé, UFR de Mathématiques, Université de Lille 1, Villeneuve d’Ascq, France)

Abstract

In this paper, we prove that we can recover the genus of a closed compact surface $S$ in $\mathbb{R}^3$ from the restriction to a generic line of the Fourier transform of the canonical measure carried by $S$. 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 $S$, allows to recover the Euler characteristic of $S$.

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Published 12 January 2017