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math.SP2026
Equivariant Steklov homogenisation and stability of spectral representations
Samuel Audet-Beaumont, Maxime Fortier Bourque, Alexandre Girouard
We prove that isolated spectral clusters preserve their finite-group representation under equivariant spectral convergence. In particular, an irreducible limiting eigenspace cannot…
math.SP2026
An elementary counterexample to Escobar's Steklov conjecture on the three-ball
Alexandre Girouard, Thomas Hélière
We give an explicit polynomial deformation of the Euclidean metric on the unit three-ball which has positive Ricci curvature and strictly convex boundary but violates Escobar's con…