Symmetry from sectional integrals for convex domains

Ramya Dutta; Suman Kumar Sahoo

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arXiv · 1812.04389

Symmetry from sectional integrals for convex domains

Ramya Dutta·Suman Kumar Sahoo

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Abstract

Let $\Omega$ be a bounded convex domain in $\mathbb{R}^n$ ($n \ge 2$). In this work, we prove that if there exists an integrable function $f$ such that it's Radon transform over $(n-1)$-dimensional hyperplanes intersecting the domain $\Omega$ is a strictly positive function of distance to the nearest parallel supporting hyperplane to $\Omega$, then $\Omega$ is a ball and the function $f$ is a unique radial function about the centre of $\Omega$.

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Ramya Dutta, Suman Kumar Sahoo. 2018-12-11. Symmetry from sectional integrals for convex domains. https://arxiv.org/abs/1812.04389

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