A massa e o centro de massa de gráficos.
| Ano de defesa: | 2017 |
|---|---|
| Autor(a) principal: | |
| Orientador(a): | |
| Banca de defesa: | |
| Tipo de documento: | Tese |
| Tipo de acesso: | Acesso aberto |
| Idioma: | por |
| Instituição de defesa: |
Não Informado pela instituição
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| Programa de Pós-Graduação: |
Não Informado pela instituição
|
| Departamento: |
Não Informado pela instituição
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| País: |
Não Informado pela instituição
|
| Palavras-chave em Português: | |
| Link de acesso: | http://www.repositorio.ufc.br/handle/riufc/29086 |
Resumo: | In this thesis, masses of asymptotically flat and asymptotically hyperbolic graphs are computed as volume integrals on the manifolds. This is done by using the mass definition via Einstein’s tensor and applying the divergence theorem. A brief digression is made and an expression for the center of mass of an asymptotically flat graph is presented. The positive mass and Penrose inequalities are considered in this thesis. The validity of these inequalities are proved for the special cases we are considering. For the proof of the Penrose inequality, the boundary term of the integral that expresses the mass is computed and known results, like the Alexandrov-Fenchel inequality, are used. This thesis is supported on the works of Lam, for codimension one asymptotically flat graphs, of Mirandola-Vit´orio, for arbitrary codimension asymptotically flat graphs, and the works of Dahl-Gicquaud-Sakovich and de Lima-Gir˜ao for codimension one hyperbolic graphs. |
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Grangeiro Filho, AntônioGirão, Frederico Vale2018-01-19T12:35:27Z2018-01-19T12:35:27Z2017-10-30GRANGEIRO FILHO, A. A massa e o centro de massa de gráficos. 2017. 44 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017.http://www.repositorio.ufc.br/handle/riufc/29086In this thesis, masses of asymptotically flat and asymptotically hyperbolic graphs are computed as volume integrals on the manifolds. This is done by using the mass definition via Einstein’s tensor and applying the divergence theorem. A brief digression is made and an expression for the center of mass of an asymptotically flat graph is presented. The positive mass and Penrose inequalities are considered in this thesis. The validity of these inequalities are proved for the special cases we are considering. For the proof of the Penrose inequality, the boundary term of the integral that expresses the mass is computed and known results, like the Alexandrov-Fenchel inequality, are used. This thesis is supported on the works of Lam, for codimension one asymptotically flat graphs, of Mirandola-Vit´orio, for arbitrary codimension asymptotically flat graphs, and the works of Dahl-Gicquaud-Sakovich and de Lima-Gir˜ao for codimension one hyperbolic graphs.Neste trabalho, calculam-se as massas de gráficos assintoticamente planos e assintoticamente hiperbólicos como integrais de volume sobre as variedades. Isto é feito partindo-se da definição de massa via tensor de Einstein e aplicando-se o teorema da divergência. É apresentada uma expressão para o centro de massa de um gráfico assintoticamente plano. Faz-se presente neste trabalho a conjectura da massa positiva e a desigualdades de Penrose. Demonstra-se a veracidade destas para os casos particulares que estamos considerando. Para a demonstração da desigualdade de Penrose, calcula-se o termo de bordo da integral que expressa a massa e recorre-se a resultados conhecidos, como a desigualdade de Alexandrov-Fenchel. Toma-se por base os trabalhos realizados por Lam, para gráficos assintoticamente planos de codimensão um, por Mirandola-Vitório, para gráficos assintoticamente planos de codimensão arbitrária, e os trabalhos de Dahl-Gicquaud-Sakovich e de de Lima-Girão para gráficos hiperbólicos de codimensão um.MassaCentro de massaGráficos assintoticamente planosGráficos assintoticamente hiperbólicosDesigualdade da massa positivaDesigualdade de PenroseMassCenter of massAsymptotically flat graphsAsymptotically hyperbolic graphsPositive mass inequalityPenrose inequalityA massa e o centro de massa de gráficos.The mass and center of mass of graphs.info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisporreponame:Repositório Institucional da Universidade Federal do Ceará (UFC)instname:Universidade Federal do Ceará (UFC)instacron:UFCinfo:eu-repo/semantics/openAccessORIGINAL2017_tese_agrangeirofilho.pdf2017_tese_agrangeirofilho.pdfapplication/pdf360393http://repositorio.ufc.br/bitstream/riufc/29086/3/2017_tese_agrangeirofilho.pdf8ad9245fa85cd718bbba70eba16ffe83MD53LICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://repositorio.ufc.br/bitstream/riufc/29086/4/license.txt8a4605be74aa9ea9d79846c1fba20a33MD54riufc/290862019-01-04 10:22:44.681oai:repositorio.ufc.br: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Repositório InstitucionalPUBhttp://www.repositorio.ufc.br/ri-oai/requestbu@ufc.br || repositorio@ufc.bropendoar:2019-01-04T13:22:44Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)false |
| dc.title.pt_BR.fl_str_mv |
A massa e o centro de massa de gráficos. |
| dc.title.en.pt_BR.fl_str_mv |
The mass and center of mass of graphs. |
| title |
A massa e o centro de massa de gráficos. |
| spellingShingle |
A massa e o centro de massa de gráficos. Grangeiro Filho, Antônio Massa Centro de massa Gráficos assintoticamente planos Gráficos assintoticamente hiperbólicos Desigualdade da massa positiva Desigualdade de Penrose Mass Center of mass Asymptotically flat graphs Asymptotically hyperbolic graphs Positive mass inequality Penrose inequality |
| title_short |
A massa e o centro de massa de gráficos. |
| title_full |
A massa e o centro de massa de gráficos. |
| title_fullStr |
A massa e o centro de massa de gráficos. |
| title_full_unstemmed |
A massa e o centro de massa de gráficos. |
| title_sort |
A massa e o centro de massa de gráficos. |
| author |
Grangeiro Filho, Antônio |
| author_facet |
Grangeiro Filho, Antônio |
| author_role |
author |
| dc.contributor.author.fl_str_mv |
Grangeiro Filho, Antônio |
| dc.contributor.advisor1.fl_str_mv |
Girão, Frederico Vale |
| contributor_str_mv |
Girão, Frederico Vale |
| dc.subject.por.fl_str_mv |
Massa Centro de massa Gráficos assintoticamente planos Gráficos assintoticamente hiperbólicos Desigualdade da massa positiva Desigualdade de Penrose Mass Center of mass Asymptotically flat graphs Asymptotically hyperbolic graphs Positive mass inequality Penrose inequality |
| topic |
Massa Centro de massa Gráficos assintoticamente planos Gráficos assintoticamente hiperbólicos Desigualdade da massa positiva Desigualdade de Penrose Mass Center of mass Asymptotically flat graphs Asymptotically hyperbolic graphs Positive mass inequality Penrose inequality |
| description |
In this thesis, masses of asymptotically flat and asymptotically hyperbolic graphs are computed as volume integrals on the manifolds. This is done by using the mass definition via Einstein’s tensor and applying the divergence theorem. A brief digression is made and an expression for the center of mass of an asymptotically flat graph is presented. The positive mass and Penrose inequalities are considered in this thesis. The validity of these inequalities are proved for the special cases we are considering. For the proof of the Penrose inequality, the boundary term of the integral that expresses the mass is computed and known results, like the Alexandrov-Fenchel inequality, are used. This thesis is supported on the works of Lam, for codimension one asymptotically flat graphs, of Mirandola-Vit´orio, for arbitrary codimension asymptotically flat graphs, and the works of Dahl-Gicquaud-Sakovich and de Lima-Gir˜ao for codimension one hyperbolic graphs. |
| publishDate |
2017 |
| dc.date.issued.fl_str_mv |
2017-10-30 |
| dc.date.accessioned.fl_str_mv |
2018-01-19T12:35:27Z |
| dc.date.available.fl_str_mv |
2018-01-19T12:35:27Z |
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info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/doctoralThesis |
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doctoralThesis |
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publishedVersion |
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GRANGEIRO FILHO, A. A massa e o centro de massa de gráficos. 2017. 44 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017. |
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http://www.repositorio.ufc.br/handle/riufc/29086 |
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GRANGEIRO FILHO, A. A massa e o centro de massa de gráficos. 2017. 44 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017. |
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http://www.repositorio.ufc.br/handle/riufc/29086 |
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por |
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por |
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