Liouville-Type Theorems for CC-F-Harmonic Maps into a Carnot Group
Liouville-Type Theorems for CC-F-Harmonic Maps into a Carnot Group
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DOI：
10.1007/s12220-020-00424-z
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发表时间：
2020-05
期刊：
影响因子：
--
通讯作者：
Guoqing He;Jing Li;P. Zhao
中科院分区：
文献类型：
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作者：
Guoqing He;Jing Li;P. Zhao
本文给出了黎曼流形到卡诺群映射的一个水平能量泛函。该泛函的临界映射称为ascc - f调和映射。在距离函数的Hessian和ofF(t)度的适当条件下，通过假设水平能量的增长条件或映射在无穷远处的渐近条件，得到了从完备黎曼流形到卡诺群的cc - f调和映射的几个liouville型定理。
In this paper, we introduce a horizontalF-energy functional for maps from a Riemannian manifold to a Carnot group. The critical maps of this functional are referred to asCC-F-harmonic maps. Under suitable conditions on the Hessian of the distance function and the degree ofF(t), we obtain several Liouville-type theorems forCC-F-harmonic maps from some complete Riemannian manifolds to Carnot groups by assuming either growth condition of the horizontalF-energy or an asymptotic condition at the infinity for the maps.