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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1802.01010 |
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Table of Contents:
- Let $M$ be a $C^2$-smooth Riemannian manifold with boundary and $N$ a complete $C^2$-smooth Riemannian manifold. We show that each stationary $p$-harmonic mapping $u\colon M\to N$, whose image lies in a compact subset of $N$, is locally $C^{1,α}$ for some $α\in (0,1)$, provided that $N$ is simply connected and has non-positive sectional curvature. We also prove similar results for each minimizing $p$-harmonic mapping $u\colon M\to N$ with $u(M)$ being contained in a regular geodesic ball. Moreover, when $M$ has non-negative Ricci curvature and $N$ is simply connected and has non-positive sectional curvature, we deduce a quantitative gradient estimate for each $C^1$-smooth weakly $p$-harmonic mapping $u\colon M\to N$. Consequently, we obtain a Liouville-type theorem for $C^1$-smooth weakly $p$-harmonic mappings in the same setting.