A short note on the Schiffer's conjecture for a class of centrally symmetric convex domains in $\mathbb{R}^2$

Sugata Mondal

A short note on the Schiffer's conjecture for a class of centrally symmetric convex domains in $\mathbb{R}^2$

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arxiv 2311.14442 v1 pith:UYCB6L5T submitted 2023-11-24 math.AP

Sugata Mondal This is my paper · ORCID

classification math.AP

keywords omegapartialcentrallyconjecturemathbbschiffersymmetricanalytic

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abstract

Let $\Omega$ be a bounded centrally symmetric domain in $\mathbb{R}^2$ with analytic boundary $\partial \Omega$ and center $c$. Let $\tau = \tau(\Omega)$ be the number of points $p$ on $\partial \Omega$ such that the normal line to $\partial \Omega$ at $p$ passes through $c$. We show that if $\tau < 8$ then $\Omega$ satisfies the Schiffer's conjecture.

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