Jaume de Dios Pont

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20242026

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math.AP2026

Counterexamples to Schiffer's Conjecture

Gonzalo Cao-Labora, Jaume de Dios Pont

The Schiffer conjecture states that if a smooth domain $Ω \subset R^{n}$ admits a Neumann eigenfunction of the Laplacian which is constant at the boundary, then the domain is…

math.AP2024

Convex sets can have interior hot spots

Jaume de Dios Pont

The hot spots conjecture asserts that for any convex bounded domain $I^c ◯$ in $R^{d}$ , the first non-trivial Neumann eigenfunction of the Laplace operator in $I^c ◯$ attains its m…