[geometry-ml:04902] OIST Geometric PDE and Applied Analysis Seminar (10/27)

[Qing Liu]

幾何学メーリングリストの皆様

沖縄科学技術大学院大学の柳青と申します．
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柳青

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Date: Thursday, October 27, 16:00-17:00
Speaker: Kazuhiro Kuwae (Fukuoka University)
Zoom registration: https://oist.zoom.us/meeting/register/tJUpcOihqT0uGtAe4wlWD6SBoZEd4Abcaorn

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

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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