论带势次椭圆谐波映射的稳定性

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2024-04-25 DOI:10.1016/j.difgeo.2024.102143

Tian Chong , Yuxin Dong , Guilin Yang

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引用次数: 0

摘要

本文研究了带势次椭圆谐波图的稳定性问题。首先，我们推导了带势次椭圆调和映射的第一和第二变分公式。结果证明，如果目标流形的曲率为非正值，并且势的 Hessian 为非正定值，则具有势的亚椭圆谐波图是稳定的。我们还给出了梁式结果，其中涉及当目标流形是维数≥3 的球面时带势次椭圆调和映射的不稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On stability of subelliptic harmonic maps with potential

In this paper, we investigate the stability problem of subelliptic harmonic maps with potential. First, we derive the first and second variation formulas for subelliptic harmonic maps with potential. As a result, it is proved that a subelliptic harmonic map with potential is stable if the target manifold has nonpositive curvature and the Hessian of the potential is nonpositive definite. We also give Leung type results which involve the instability of subelliptic harmonic maps with potential when the target manifold is a sphere of dimension ≥3.

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.