Nonnegative Scalar Curvature and Area Decreasing Maps
Let (M, gᵀᴹ) be a noncompact complete spin Riemannian manifold of even dimension n, with kᵀᴹ denoting the associated scalar curvature. Let : M → Sⁿ(1) be a smooth area decreasing map, which is locally constant near infinity and of nonzero degree. We show that if kᵀᴹ ≥ n(n−1) on the support of d, the...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2020 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210717 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Nonnegative Scalar Curvature and Area Decreasing Maps. Weiping Zhang. SIGMA 16 (2020), 033, 7 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862731350892609536 |
|---|---|
| author | Zhang, Weiping |
| author_facet | Zhang, Weiping |
| citation_txt | Nonnegative Scalar Curvature and Area Decreasing Maps. Weiping Zhang. SIGMA 16 (2020), 033, 7 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Let (M, gᵀᴹ) be a noncompact complete spin Riemannian manifold of even dimension n, with kᵀᴹ denoting the associated scalar curvature. Let : M → Sⁿ(1) be a smooth area decreasing map, which is locally constant near infinity and of nonzero degree. We show that if kᵀᴹ ≥ n(n−1) on the support of d, then inf(kᵀᴹ) < 0. This answers a question of Gromov. We use a simple deformation of the Dirac operator to prove the result. The odd-dimensional analogue is also presented.
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| first_indexed | 2025-12-17T12:04:34Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210717 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-17T12:04:34Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Zhang, Weiping 2025-12-15T15:31:48Z 2020 Nonnegative Scalar Curvature and Area Decreasing Maps. Weiping Zhang. SIGMA 16 (2020), 033, 7 pages 1815-0659 2020 Mathematics Subject Classification: 53C27; 57R20; 58J20 arXiv:1912.03649 https://nasplib.isofts.kiev.ua/handle/123456789/210717 https://doi.org/10.3842/SIGMA.2020.033 Let (M, gᵀᴹ) be a noncompact complete spin Riemannian manifold of even dimension n, with kᵀᴹ denoting the associated scalar curvature. Let : M → Sⁿ(1) be a smooth area decreasing map, which is locally constant near infinity and of nonzero degree. We show that if kᵀᴹ ≥ n(n−1) on the support of d, then inf(kᵀᴹ) < 0. This answers a question of Gromov. We use a simple deformation of the Dirac operator to prove the result. The odd-dimensional analogue is also presented. The author would like to thank the referees for their careful reading and very helpful suggestions. This work was partially supported by NNSFC Grant no.11931007. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Nonnegative Scalar Curvature and Area Decreasing Maps Article published earlier |
| spellingShingle | Nonnegative Scalar Curvature and Area Decreasing Maps Zhang, Weiping |
| title | Nonnegative Scalar Curvature and Area Decreasing Maps |
| title_full | Nonnegative Scalar Curvature and Area Decreasing Maps |
| title_fullStr | Nonnegative Scalar Curvature and Area Decreasing Maps |
| title_full_unstemmed | Nonnegative Scalar Curvature and Area Decreasing Maps |
| title_short | Nonnegative Scalar Curvature and Area Decreasing Maps |
| title_sort | nonnegative scalar curvature and area decreasing maps |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210717 |
| work_keys_str_mv | AT zhangweiping nonnegativescalarcurvatureandareadecreasingmaps |