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Gradient estimate for exponentially harmonic functions on complete Riemannian manifolds |
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| Authors: | Jiaxian Wu Qihua Ruan Yi-Hu Yang |
| Institution: | 1. Department of Mathematics, Tongji University, Shanghai, 200092, China 2. Department of Mathematics, Putian University, Putian, 351100, Fujian, China 3. Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China |
| Abstract: | The notion of exponentially harmonic maps was introduced by Eells and Lemaire (Proceedings of the Banach Center Semester on PDE, pp. 1990–1991, 1990). In this note, by using the maximum principle we get the gradient estimate of exponentially harmonic functions, and then derive a Liouville type theorem for bounded exponentially harmonic functions on a complete Riemannian manifold with nonnegative Ricci curvature and sectional curvature bounded below. |
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