Abstract
In this note we will provide a gradient estimate for harmonic maps from a complete noncompact Riemannian manifold with compact boundary (which we call "Kasue manifold") into a simply connected complete Riemannian manifold with non-positive sectional curvature. As a consequence, we can obtain a Liouville theorem. We will also show the nonexistence of positive solutions to some linear elliptic equations on Kasue manifolds.
Funding Statement
This paper is supported by NSFC 12071352, NSFC 11721101, the National Key R and D Program of China 2020YFA0713100, and 2022CFB240.
Citation
Jun Sun. Xiaobao Zhu. "Liouville Theorem for harmonic maps from Riemannian manifold with compact boundary." Kodai Math. J. 46 (2) 207 - 218, June 2023. https://doi.org/10.2996/kmj46204
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