Energy-minimizing Mappings of Complex Projective Spaces
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909387165007872 |
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| author | Hoisington, Joseph |
| author_facet | Hoisington, Joseph |
| contents | We show that in all homotopy classes of mappings from complex projective space to Riemannian manifolds, the infimum of the energy is proportional to the infimal area in the homotopy class of mappings of the 2-sphere which represents the induced homomorphism on the second homotopy group. We then establish a family of optimal lower bounds for a larger class of energy functionals for mappings from real and complex projective space to Riemannian manifolds and characterize the mappings which attain these lower bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_08285 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Energy-minimizing Mappings of Complex Projective Spaces Hoisington, Joseph Differential Geometry Algebraic Geometry Complex Variables Primary 53C43, 53C55 Secondary 53C35 We show that in all homotopy classes of mappings from complex projective space to Riemannian manifolds, the infimum of the energy is proportional to the infimal area in the homotopy class of mappings of the 2-sphere which represents the induced homomorphism on the second homotopy group. We then establish a family of optimal lower bounds for a larger class of energy functionals for mappings from real and complex projective space to Riemannian manifolds and characterize the mappings which attain these lower bounds. |
| title | Energy-minimizing Mappings of Complex Projective Spaces |
| topic | Differential Geometry Algebraic Geometry Complex Variables Primary 53C43, 53C55 Secondary 53C35 |
| url | https://arxiv.org/abs/2311.08285 |