Instability of solutions to the Ginzburg-Landau equation on Sn and CPn

被引:6
作者
Cheng, Da Rong [1 ]
机构
[1] Univ Chicago, Dept Math, Chicago, IL 60637 USA
关键词
Ginzburg-Landau functional; Stationary varifolds in codimension two; Second variation; Morse index; STABILITY; VORTICES; CURRENTS;
D O I
10.1016/j.jfa.2020.108669
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study critical points of the Ginzburg-Landau (GL) functional and the abelian Yang-Mills-Higgs (YMH) functional on the sphere and the complex projective space, both equipped with the standard metrics. For the GL functional we prove that on S-n with n >= 2 and CPn with n >= 1, stable critical points must be constants. In addition, for GL critical points on S-n for n >= 3 we obtain a lower bound on the Morse index under suitable assumptions. On the other hand, for the abelian YMH functional we prove that on S-n with n >= 4 there are no stable critical points unless the line bundle is isomorphic to S-n x C, in which case the only stable critical points are the trivial ones. Our methods come from the work of Lawson-Simons. (C) 2020 Elsevier Inc. All rights reserved.
引用
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页数:45
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