arXiv subjects

David Lenze

Publications and source records attributed to David Lenze.

4 recordsLinked to original sources

arXiv2026

Rigidity of Wasserstein spaces over Riemannian manifolds

We show that L2 Wasserstein spaces over Riemannian manifolds are isometrically rigid if and only if their underlying Riemannian manifolds do not admit a Euclidean de Rham factor. We further show that, unless the manifold is isometric to the real line, every isometry of the Wasserstein space is shape-preserving in the sense of Kloeckner. Finally, we demonstrate that two such Wasserstein spaces are isometric if and only if their underlying Riemannian manifolds are isometric.

math.DG↗

arXiv2025

Isometries of the Ebin metric

We study the space of Riemannian metrics over a compact manifold equipped with the Ebin metric. We characterize its self-isometries and prove that two such spaces are isometric if and only if their underlying manifolds are diffeomorphic.

math.MG↗

arXiv2025

Characterization of higher rank via affine maps

We show that Hadamard spaces with geometric group actions admit affine maps that are not dilations, if and only if they are Riemannian symmetric spaces of higher rank, Euclidean buildings of higher rank, or split as non-trivial metric products.

math.MG↗

arXiv2024

Isometric rigidity of $L^2$-spaces with manifold targets

We describe the isometry group of $L^2(\Omega, M)$ for Riemannian manifolds $M$ of dimension at least two with irreducible universal cover. We establish a rigidity result for the isometries of these spaces: any isometry arises from an automorphism of $\Omega$ and a family of isometries of $M$, distinguishing these spaces from the classical $L^2(\Omega)$. Additionally, we prove that these spaces lack irreducible factors and that two such spaces are isometric if and only if the underlying manifolds are.

math.MG↗