Uma demonstração probabilística do teorema de Cheng-Liouville
The following theorem due to S.-Y.Cheng [6]: Let f: M → N be a harmonic map, where M and N are complete Riemannian manifolds. Suppose that M has nonnegative Ricci curvature, N has nonpositive sectional curvature, and N is simply connected. If f has sublinear asymptotic growth, then f must be a...
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| Tipo de documento: | Tesis de maestría |
| Estado: | Published version |
| Fecha de publicación: | 2008 |
| País: | Brasil |
| Institución: | UEM |
| Repositorio: | Repositório Institucional da Universidade Estadual de Maringá (RI-UEM) |
| Lenguaje: | Portugués |
| OAI Identifier: | oai:localhost:1/5519 |
| Acceso en línea: | http://repositorio.uem.br:8080/jspui/handle/1/5519 |
| Nivel de acceso: | Acceso abierto |
| Palabra clave: | Teorema de Cheng-Liouville Geometria Riemanniana Teorema da comparação de Bishop Cálculo estocástico Movimento browniano Ciências Exatas e da Terra Matemática |
| Sumario: | The following theorem due to S.-Y.Cheng [6]: Let f: M → N be a harmonic map, where M and N are complete Riemannian manifolds. Suppose that M has nonnegative Ricci curvature, N has nonpositive sectional curvature, and N is simply connected. If f has sublinear asymptotic growth, then f must be a constant map. There is a probabilistic proof of this theorem due to the Seth Stafford [25]. The aim of this work is to reproduce this proof with details for the case N = Rn |
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