Existence and Stability of α−Harmonic Maps
In this paper, we first study the α−energy functional, Euler-Lagrange operator, and α-stress-energy tensor. Second, it is shown that the critical points of the α−energy functional are explicitly related to harmonic maps through conformal deformation. In addition, an α−harmonic map is constructed fro...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/1906905 |
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| author | Seyed Mehdi Kazemi Torbaghan Keyvan Salehi Salman Babayi |
| author_facet | Seyed Mehdi Kazemi Torbaghan Keyvan Salehi Salman Babayi |
| author_sort | Seyed Mehdi Kazemi Torbaghan |
| collection | DOAJ |
| description | In this paper, we first study the α−energy functional, Euler-Lagrange operator, and α-stress-energy tensor. Second, it is shown that the critical points of the α−energy functional are explicitly related to harmonic maps through conformal deformation. In addition, an α−harmonic map is constructed from any smooth map between Riemannian manifolds under certain assumptions. Next, we determine the conditions under which the fibers of horizontally conformal α−harmonic maps are minimal submanifolds. Then, the stability of any α−harmonic map on Riemannian manifold with nonpositive curvature is studied. Finally, the instability of α−harmonic maps from a compact manifold to a standard unit sphere is investigated. |
| format | Article |
| id | doaj-art-6060e6e5a1744bf09e8b99ce2d9319fd |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-6060e6e5a1744bf09e8b99ce2d9319fd2025-08-20T02:35:19ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/1906905Existence and Stability of α−Harmonic MapsSeyed Mehdi Kazemi Torbaghan0Keyvan Salehi1Salman Babayi2Department of MathematicsCentre of Theoretical Chemistry and Physics (CTCP)Department of MathematicsIn this paper, we first study the α−energy functional, Euler-Lagrange operator, and α-stress-energy tensor. Second, it is shown that the critical points of the α−energy functional are explicitly related to harmonic maps through conformal deformation. In addition, an α−harmonic map is constructed from any smooth map between Riemannian manifolds under certain assumptions. Next, we determine the conditions under which the fibers of horizontally conformal α−harmonic maps are minimal submanifolds. Then, the stability of any α−harmonic map on Riemannian manifold with nonpositive curvature is studied. Finally, the instability of α−harmonic maps from a compact manifold to a standard unit sphere is investigated.http://dx.doi.org/10.1155/2022/1906905 |
| spellingShingle | Seyed Mehdi Kazemi Torbaghan Keyvan Salehi Salman Babayi Existence and Stability of α−Harmonic Maps Journal of Mathematics |
| title | Existence and Stability of α−Harmonic Maps |
| title_full | Existence and Stability of α−Harmonic Maps |
| title_fullStr | Existence and Stability of α−Harmonic Maps |
| title_full_unstemmed | Existence and Stability of α−Harmonic Maps |
| title_short | Existence and Stability of α−Harmonic Maps |
| title_sort | existence and stability of α harmonic maps |
| url | http://dx.doi.org/10.1155/2022/1906905 |
| work_keys_str_mv | AT seyedmehdikazemitorbaghan existenceandstabilityofaharmonicmaps AT keyvansalehi existenceandstabilityofaharmonicmaps AT salmanbabayi existenceandstabilityofaharmonicmaps |