On the Effectless Cut Method for Laplacian Eigenvalues in any dimensions

Vincenzo Amato; Nunzia Gavitone; Francesca de Giovanni

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arXiv · 2604.00976

On the Effectless Cut Method for Laplacian Eigenvalues in any dimensions

Vincenzo Amato·Nunzia Gavitone·Francesca de Giovanni

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Abstract

In this paper, we study the optimization of the first Laplacian eigenvalue on axisymmetric doubly connected domains under positive Robin boundary conditions. Under additional geometric constraints, we prove that spherical shells maximize this eigenvalue. Our approach combines known isoperimetric inequalities for mixed Laplacian eigenvalues with a higher-dimensional extension of the effectless cut technique introduced by Hersch to study multiply connected membranes of given area fixed along their boundaries.

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Vincenzo Amato, Nunzia Gavitone, Francesca de Giovanni. 2026-04-01. On the Effectless Cut Method for Laplacian Eigenvalues in any dimensions. https://arxiv.org/abs/2604.00976

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