Lipschitz continuity and Bochner-Eells-Sampson inequality for harmonic maps from RCD(K,N) spaces to CAT(0) spaces

Journal article

We establish Lipschitz regularity of harmonic maps from RCD(K, N) metric measure spaces with lower Ricci curvature bounds and dimension upper bounds in synthetic sense with values into CAT(0) metric spaces with non-positive sectional curvature. Under the same assumptions, we obtain a Bochner-Eells-Sampson inequality with a Hessian type-term. This gives a fairly complete generalization of the classical theory for smooth source and target spaces to their natural synthetic counterparts and an af...

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Authors: Mondino, A; Semola, D

• Publication status: Accepted
• Peer review status: Peer reviewed
• Publisher: Johns Hopkins University Press
• Journal: American Journal of Mathematics
• Acceptance date: 2023-11-03
• EISSN: 1080-6377
• ISSN: 0002-9327
• Language: English