Global uniqueness of the minimal sphere in the Atiyah--Hitchin manifold

Chung-Jun Tsai National Taiwan University Mu-Tao Wang Columbia University

Analysis of PDEs Differential Geometry Geometric Analysis and Geometric Topology Mathematical Physics mathscidoc:1804.03011

In this note, we study submanifold geometry of the Atiyah--Hitchin manifold, a double cover of the 2-monopole moduli space, which plays an important role in various settings such as the supersymmetric background of string theory. When the manifold is naturally identified as the total space of a line bundle over S^2, the zero section is a distinguished minimal 2-sphere of considerable interest. In particular, there has been a conjecture about the uniqueness of this minimal 2-sphere among all closed minimal 2-surfaces. We show that this minimal 2-sphere satisfies the ``strong stability condition" proposed in our earlier work, and confirm the global uniqueness as a corollary.
minimal surface, hyperKahler geometry, Atiyah-Hitchin manifold
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  • arXiv:1804.08201
@inproceedings{chung-junglobal,
  title={Global uniqueness of the minimal sphere in the Atiyah--Hitchin manifold},
  author={Chung-Jun Tsai, and Mu-Tao Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180430143809095985082},
}
Chung-Jun Tsai, and Mu-Tao Wang. Global uniqueness of the minimal sphere in the Atiyah--Hitchin manifold. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180430143809095985082.
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