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math.DG2025
Zoll manifolds with boundary
Eduardo Longa, Paolo Piccione, Roney Santos
We introduce and study Zoll manifolds with boundary: compact Riemannian manifolds with smooth boundary such that every geodesic issuing orthogonally from the boundary returns ortho…
math.DG2023
Extremal metrics for the eigenvalues of the Laplacian on manifolds with boundary
Eduardo Longa
We show there are no extremal metrics for the eigenvalues of the Neumann Laplacian on any compact manifold. Nonetheless, we construct examples of conformally extremal metrics for t…
math.DG2019
Sharp systolic inequalities for -manifolds with boundary
Eduardo Longa
We prove some sharp systolic inequalities for compact -manifolds with boundary. They relate the (relative) homological systoles of the manifold to its scalar curvature and mean…