Author

Siavash Sadeghi

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Preprint Sep 2026

A counterexample to Kenig's conjecture for the Laplace double-layer operator

We disprove Kenig's 1994 spectral-radius conjecture for the double-layer operator in every dimension $d\ge2$. For every $t>1/2$ sufficiently close to $1/2$, we construct a bounded simply connected Lipschitz domain with connected boundary such that the double-layer operator on $L^2$ with respect to the surface measure h...

Matthew J. Colbrook, Siavash Sadeghi · 0 citations

Preprint Aug 2026

A computer-assisted counterexample to the planar Berenstein conjecture

The Dirichlet endpoint considered here, the nonzero Neumann datum forces the harmonic source modes to remain, producing a coupled interior--boundary system involving the full zero-Dirichlet inverse and its Neumann trace, together with a separate sign-recovery problem.

Matthew J. Colbrook, Siavash Sadeghi, George Stepaniants · 1 citation

Preprint Aug 2026

A sharp isoperimetric inequality for the Neumann--Poincar\'e operator in every dimension

Let $\Omega\subset\mathbb{R}^d$, $d\ge2$, be a bounded connected domain with boundary of class $C^{1,\alpha}$, where $0<\alpha<1$. For the adjoint Neumann--Poincar\'e operator $K^*_{\partial\Omega}$, normalised so that its distinguished eigenvalue is $1/2$, let $\lambda_j^+(\Omega)$ denote the upper min--max values on...

Matthew J. Colbrook, Siavash Sadeghi · 0 citations