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Author

George Stepaniants

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2 papers indexed here

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Preprint Aug 2026

A computer-assisted counterexample to the planar Berenstein conjecture

Recent work of Colbrook and Stepaniants produced the first counterexamples to the planar Pompeiu and Schiffer conjectures and introduced the conformal fixed-disc, disk-polynomial, and validated-tail machinery used here. By adapting this framework to the complementary Dirichlet endpoint, we disprove the unrestricted pla...

Matthew J. Colbrook, Siavash Sadeghi, George Stepaniants · 0 citations
Preprint Aug 2026

A computer-assisted counterexample to the planar Pompeiu and Schiffer conjectures

A bounded simply connected noncircular domain of $\Omega$ with real-analytic Jordan boundary and a nonconstant function $u$ such that $u$ is a Neumann eigenfunction which is constant on the boundary, and $\Omega$ is a counterexample to Schiffer's conjecture.

Matthew J. Colbrook, George Stepaniants · 5 citations

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