环面作用于S^n及保形不变方程的变符号解

M. Pino, M. Musso, F. Pacard, A. Pistoia
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引用次数: 74

摘要

-构造了n≥4时定义在Sn中的共形不变半线性椭圆方程的变符号解序列。我们得到的解能量大,并且集中在Sn的一些特殊子流形上。例如,当n≥4时,我们得到一系列的解,这些解的能量集中在一个大圆或有限多个连接的大圆上(它们对应于嵌入在S3 × {0} Sn中的Hopf链接)。在维数n≥5中,我们得到能量集中在二维环面(对应于嵌入在S3 × {0} Sn中的Clifford环面)上的解序列。
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Torus action on S^n and sign changing solutions for conformally invariant equations
— We construct sequences of sign changing solutions for some conformally invariant semilinear elliptic equation which is defined in Sn, when n ≥ 4. The solutions we obtain have large energy and concentrate along some special submanifolds of Sn. For example, when n ≥ 4, we obtain sequences of solutions whose energy concentrates along one great circle or finitely many great circles which are linked (they correspond to Hopf links embedded in S3 × {0} ⊂ Sn). In dimension n ≥ 5, we obtain sequences of solutions whose energy concentrates along a two dimensional torus (which corresponds to a Clifford torus embedded in S3 × {0} ⊂ Sn).
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来源期刊
CiteScore
2.30
自引率
0.00%
发文量
90
审稿时长
>12 weeks
期刊介绍: The Annals of the Normale Superiore di Pisa, Science Class, publishes papers that contribute to the development of Mathematics both from the theoretical and the applied point of view. Research papers or papers of expository type are considered for publication. The Annals of the Normale Scuola di Pisa - Science Class is published quarterly Soft cover, 17x24
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