[Seminar] "Liouville theorem for V-harmonic maps under non-negative (m, V)-Ricci curvature for non-positive m" by Prof. Kazuhiro Kuwae

Geometric PDE and Applied Analysis Seminar (October 27, 2022)

Title: Liouville theorem for \(V\)-harmonic maps under non-negative \((m, V)\)-Ricci curvature for non-positive \(m\)

Speaker: Prof. Kauzhiro Kuwae (Fukouka University)

Abstract: This talk is based on a joint work with Xiangdong Li (CAS AMSS), Songzi Li (Renming University of China) and Yohei Sakurai (Saitama University). We consider a generalization of bounded Liouville property for \(V \)-harmonic maps under non-negative Ricci curvature in terms of \(m\)-Bakry-Émery Ricci tensor for non-positive \(m\). This condition is quite weaker than the non-negativity of  usual \(m\)-Bakry-Émery Ricci curvature for which \(m\) is greater than the dimension \(n\) of the source Riemannian manifold. We establish a Liouville type theorem of \(V\)-harmonic maps into Hadamard manifolds having a growth condition which depends on the shape of \(V\)-Laplacian comparison theorem under such non-negative \(m\)-Bakry-Émery Ricci curvature. We prove the result by use of stochastic analysis. Of course, one can prove the result by purely geometric analysis.

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