Rigidez de planos projetivos minimizantes de área em 3-Variedades
In this work, we talk about the article "Area-Minimizing Projective Planes in 3- Manifolds" due to Hubert Bray, Simon Brendle, Michael Eichmair and Andr´e Neves. In this article they consider a compact Riemannian 3-manifold (M; g) with positive scalar curvature and an embedded projective p...
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| Format: | master thesis |
| Status: | Published version |
| Publication Date: | 2016 |
| Country: | Brasil |
| Institution: | Universidade Federal do Maranhão (UFMA) |
| Repository: | Biblioteca Digital de Teses e Dissertações da UFMA |
| Language: | Portuguese |
| OAI Identifier: | oai:tede2:tede/1615 |
| Online Access: | http://tedebc.ufma.br:8080/jspui/handle/tede/1615 |
| Access Level: | Open access |
| Keyword: | Variedade Riemanniana Plano projetivo minimizante Superfície mínima Riemanniana manifold Minimizing Projective Plan Minimal surface Matemática |
| Summary: | In this work, we talk about the article "Area-Minimizing Projective Planes in 3- Manifolds" due to Hubert Bray, Simon Brendle, Michael Eichmair and Andr´e Neves. In this article they consider a compact Riemannian 3-manifold (M; g) with positive scalar curvature and an embedded projective plane. In these conditions they prove a higher estimate of curvature, in term of infimum of the scalar curvature of (M; g), for the area of the projective plane that has the smallest area within the class of all surfaces Σ ⊂ M homeomorphic to projective plane. Furthermore, they prove that this inequality is great. More precisely, they get that if this equality hold in (M 3; g), so M is isometric to the three-dimensional projective space RP3 with constant sectional curvature. |
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