Infinitely many non-ball planar domains carry Neumann eigenfunctions that are constant on the boundary, so Schiffer's and Pompeiu's conjectures are false in R^2.
Canuto,Stability results for theN-dimensional Schiffer conjecture via a perturbation method, Calc
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
citation-role summary
baseline 1
citation-polarity summary
fields
math.AP 1years
2026 1verdicts
CONDITIONAL 1roles
baseline 1polarities
baseline 1representative citing papers
citing papers explorer
-
Counterexamples to Schiffer's Conjecture
Infinitely many non-ball planar domains carry Neumann eigenfunctions that are constant on the boundary, so Schiffer's and Pompeiu's conjectures are false in R^2.