Symmetry from sectional integrals for convex domains

2018/12/11 by Dutta, Ramya, Sahoo, Suman Kumar
#44A12 #53C65 #65R32 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.04389

Abstract

Let Ω be a bounded convex domain in ℝⁿ (n ≥ 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 Ω is a strictly positive function of distance to the nearest parallel supporting hyperplane to Ω, then Ω is a ball and the function f is a unique radial function about the centre of Ω.

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