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<p>Let Ω be a bounded centrally symmetric domain in ℝ<sup>2</sup> with analytic boundary ∂Ω and center <i>c</i>. Let <i>τ</i> = <i>τ</i>(Ω) be the number of points <i>p</i> on <i>∂</i>Ω such that the normal line to <i>∂</i>Ω at <i>p</i> passes through <i>c</i>. We show that if <i>τ</i> &lt; 8 then Ω satisfies Schiffer’s conjecture.</p>

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A short note on Schiffer’s conjecture for a class of centrally symmetric convex domains in ℝ2

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  • 发表日期：

    2025年12月15日

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  • Sugata Mondal

摘要

Let Ω be a bounded centrally symmetric domain in ℝ2 with analytic boundary ∂Ω and center c. Let τ = τ(Ω) be the number of points p on ∂Ω such that the normal line to ∂Ω at p passes through c. We show that if τ < 8 then Ω satisfies Schiffer’s conjecture.