A Generalized Bochner Technique and Its Application to the Study of Conformal Mappings
This article is devoted to geometrical aspects of conformal mappings of complete Riemannian and Kählerian manifolds and uses the Bochner technique, one of the oldest and most important techniques in modern differential geometry. A feature of this article is that the results presented here are easily...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/10/4/333 |
| _version_ | 1797506573994557440 |
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| author | Vladimir Rovenski Sergey Stepanov Irina Tsyganok |
| author_facet | Vladimir Rovenski Sergey Stepanov Irina Tsyganok |
| author_sort | Vladimir Rovenski |
| collection | DOAJ |
| description | This article is devoted to geometrical aspects of conformal mappings of complete Riemannian and Kählerian manifolds and uses the Bochner technique, one of the oldest and most important techniques in modern differential geometry. A feature of this article is that the results presented here are easily obtained using a generalized version of the Bochner technique due to theorems on the connection between the geometry of a complete Riemannian manifold and the global behavior of its subharmonic, superharmonic, and convex functions. |
| first_indexed | 2024-03-10T04:34:28Z |
| format | Article |
| id | doaj.art-2a40c96fc1cd4610b6e9caf985c9ea08 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T04:34:28Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-2a40c96fc1cd4610b6e9caf985c9ea082023-11-23T03:50:14ZengMDPI AGAxioms2075-16802021-12-0110433310.3390/axioms10040333A Generalized Bochner Technique and Its Application to the Study of Conformal MappingsVladimir Rovenski0Sergey Stepanov1Irina Tsyganok2Department of Mathematics, University of Haifa, Mount Carmel, Haifa 3498838, IsraelDepartment of Mathematics, Finance University, 49-55, Leningradsky Prospect, 125468 Moscow, RussiaDepartment of Mathematics, Finance University, 49-55, Leningradsky Prospect, 125468 Moscow, RussiaThis article is devoted to geometrical aspects of conformal mappings of complete Riemannian and Kählerian manifolds and uses the Bochner technique, one of the oldest and most important techniques in modern differential geometry. A feature of this article is that the results presented here are easily obtained using a generalized version of the Bochner technique due to theorems on the connection between the geometry of a complete Riemannian manifold and the global behavior of its subharmonic, superharmonic, and convex functions.https://www.mdpi.com/2075-1680/10/4/333Bochner techniqueRiemannian and Kähler manifoldsconformal diffeomorphismLiouville-type theoremscalar curvatureparacomplex structure |
| spellingShingle | Vladimir Rovenski Sergey Stepanov Irina Tsyganok A Generalized Bochner Technique and Its Application to the Study of Conformal Mappings Axioms Bochner technique Riemannian and Kähler manifolds conformal diffeomorphism Liouville-type theorem scalar curvature paracomplex structure |
| title | A Generalized Bochner Technique and Its Application to the Study of Conformal Mappings |
| title_full | A Generalized Bochner Technique and Its Application to the Study of Conformal Mappings |
| title_fullStr | A Generalized Bochner Technique and Its Application to the Study of Conformal Mappings |
| title_full_unstemmed | A Generalized Bochner Technique and Its Application to the Study of Conformal Mappings |
| title_short | A Generalized Bochner Technique and Its Application to the Study of Conformal Mappings |
| title_sort | generalized bochner technique and its application to the study of conformal mappings |
| topic | Bochner technique Riemannian and Kähler manifolds conformal diffeomorphism Liouville-type theorem scalar curvature paracomplex structure |
| url | https://www.mdpi.com/2075-1680/10/4/333 |
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