collaborators

4 papers

math.SP2026

Harmonic-Einstein maps and critical metrics for eigenvalues of the conformal Laplacian

Mehdi Eddaoudi

We prove that Clarke critical metrics for the ratio of the first two eigenvalues of the conformal Laplacian on a closed manifold with positive Yamabe constant correspond to harmoni…

math.SP2025

Payne-Pólya-Weinberger inequalities on closed Riemannian manifolds

Mehdi Eddaoudi

Payne-Pólya-Weinberger inequalities are known to be exclusive to bounded Euclidean domains with Dirichlet boundary condition. In this paper, we discuss the corresponding inequaliti…

math.SP2025

Lower bounds for the sum of the reciprocals of eigenvalues of bounded domains in , spheres, and closed orientable surfaces

Mehdi Eddaoudi

We establish lower bounds for the sum of the reciprocals of eigenvalues of the Laplacian. For bounded domains, our result extends the upper bound provided by Bucur and Henrot on th…

math.SP2025

Upper bounds for the second nonzero eigenvalue of the Laplacian via folding and conformal volume

Mehdi Eddaoudi, Alexandre Girouard

We prove an upper bound for the volume-normalized second nonzero eigenvalue of the Laplace operator on closed Riemannian manifold, in terms of the conformal volume. This bound prov…