Liouville Theorem for Harmonic Maps from Riemannian Manifold with Compact Boundary
Differential Geometry
2023-04-06 v1
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 equation on Kasue manifold.
Keywords
Cite
@article{arxiv.2304.02375,
title = {Liouville Theorem for Harmonic Maps from Riemannian Manifold with Compact Boundary},
author = {Jun Sun and Xiaobao Zhu},
journal= {arXiv preprint arXiv:2304.02375},
year = {2023}
}
Comments
12 pages, to appear on Kodai Math. J