A family of examples of harmonic maps into the sphere with one point singularity
The radial map u(x)=x‖x‖is a well-known example of a harmonic map into the spheres with a point singularity at x=0. In our previous paper (Misawa and Nakauchi, 2022) we give two examples of harmonic maps into the standard spheres of higher dimension with a singularity of a polynomial of x1‖x‖,⋯xm‖x‖...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-11-01
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| Series: | Examples and Counterexamples |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666657X23000095 |
| Summary: | The radial map u(x)=x‖x‖is a well-known example of a harmonic map into the spheres with a point singularity at x=0. In our previous paper (Misawa and Nakauchi, 2022) we give two examples of harmonic maps into the standard spheres of higher dimension with a singularity of a polynomial of x1‖x‖,⋯xm‖x‖of degree 2 and degree 3 respectively. In Fujioka (2020) uses our arguments to give an example of a harmonic map into the sphere with a singularity of a polynomial of degree 4. In this paper we give a family of examples of harmonic maps with a point singularity of a polynomial of higher degree. |
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| ISSN: | 2666-657X |