Removable sets and Lp-uniqueness on manifolds and metric measure spaces

Hinz, M.; Masamune, J.; Suzuki, K.

Abstract

We study symmetric diffusion operators on metric measure spaces. Our main question is whether essential self-adjointness or -uniqueness are preserved under the removal of a small closed set from the space. We provide characterizations of the critical size of removed sets in terms of capacities and Hausdorff dimension without any further assumption on removed sets. As a key tool we prove a non-linear truncation result for potentials of nonnegative functions. Our results are robust enough to be applied to Laplace operators on general Riemannian manifolds as well as sub-Riemannian manifolds and metric measure spaces satisfying curvature-dimension conditions. For non-collapsing Ricci limit spaces with two-sided Ricci curvature bounds we observe that the self-adjoint Laplacian is already fully determined by the classical Laplacian on the regular part.

Citation

Hinz, M., Masamune, J., & Suzuki, K. (2023). Removable sets and Lp-uniqueness on manifolds and metric measure spaces. Nonlinear Analysis: Theory, Methods and Applications, 234, https://doi.org/10.1016/j.na.2023.113296

• Journal Article Type: Article
• Acceptance Date: Apr 18, 2023
• Online Publication Date: May 13, 2023
• Publication Date: 2023
• Deposit Date: May 17, 2023
• Publicly Available Date: May 17, 2023
• Journal: Nonlinear Analysis
• Print ISSN: 0362-546X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 234
• DOI: https://doi.org/10.1016/j.na.2023.113296