The Ricci flow on a cylinder
In this paper we study the Ricci flow on surfaces homeomorphic to a cylinder (that is, a product of the circle with a compact interval). We prove longtime existence results, results on the asymptotic behavior of the flow, and we report on an interesting phenomenon: convergence to constant curvature...
- Autores:
-
Cortissoz, Jean C.
Murcia, Alexander
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2017
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/66433
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/66433
http://bdigital.unal.edu.co/67461/
- Palabra clave:
- 51 Matemáticas / Mathematics
Ricci flow
blow-up
convergence
Flujo de Ricci
explosión
convergencia
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Cortissoz, Jean C.12acd766-2678-4115-a2db-4c15379dd050300Murcia, Alexandere9f04b1e-145d-4150-bbb9-89b7fe0ce4993002019-07-03T02:07:08Z2019-07-03T02:07:08Z2017-07-01ISSN: 2357-4100https://repositorio.unal.edu.co/handle/unal/66433http://bdigital.unal.edu.co/67461/In this paper we study the Ricci flow on surfaces homeomorphic to a cylinder (that is, a product of the circle with a compact interval). We prove longtime existence results, results on the asymptotic behavior of the flow, and we report on an interesting phenomenon: convergence to constant curvature in the normalised flow, under certain assumptions on the initial data, cannot be exponential.En este artículo estudiamos el flujo de Ricci en superficies homeomorfas al cilindro (esto es, el producto de un círculo con un intervalo compacto). Al respecto, demostramos teoremas de existencia para todo tiempo de las soluciones asumiendo cierta simetría, teoremas sobre comportamiento asintótico, y reportamos un fenómeno interesante: la convergencia a curvatura constante en el flujo normalizado, bajo ciertas restricciones impuestas a la condición inicial, no puede ser exponencial.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas - Sociedad Colombiana de Matemáticashttps://revistas.unal.edu.co/index.php/recolma/article/view/70903Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasCortissoz, Jean C. and Murcia, Alexander (2017) The Ricci flow on a cylinder. Revista Colombiana de Matemáticas, 51 (2). pp. 241-257. ISSN 2357-410051 Matemáticas / MathematicsRicci flowblow-upconvergenceFlujo de RicciexplosiónconvergenciaThe Ricci flow on a cylinderArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL70903-375022-1-SM.pdfapplication/pdf386518https://repositorio.unal.edu.co/bitstream/unal/66433/1/70903-375022-1-SM.pdf204a8652e60a379a15cc52df797fa1e3MD51THUMBNAIL70903-375022-1-SM.pdf.jpg70903-375022-1-SM.pdf.jpgGenerated Thumbnailimage/jpeg5211https://repositorio.unal.edu.co/bitstream/unal/66433/2/70903-375022-1-SM.pdf.jpgad43dc7c5a1bcd3986ee01f175e51808MD52unal/66433oai:repositorio.unal.edu.co:unal/664332023-05-24 23:03:22.848Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co |
| dc.title.spa.fl_str_mv |
The Ricci flow on a cylinder |
| title |
The Ricci flow on a cylinder |
| spellingShingle |
The Ricci flow on a cylinder 51 Matemáticas / Mathematics Ricci flow blow-up convergence Flujo de Ricci explosión convergencia |
| title_short |
The Ricci flow on a cylinder |
| title_full |
The Ricci flow on a cylinder |
| title_fullStr |
The Ricci flow on a cylinder |
| title_full_unstemmed |
The Ricci flow on a cylinder |
| title_sort |
The Ricci flow on a cylinder |
| dc.creator.fl_str_mv |
Cortissoz, Jean C. Murcia, Alexander |
| dc.contributor.author.spa.fl_str_mv |
Cortissoz, Jean C. Murcia, Alexander |
| dc.subject.ddc.spa.fl_str_mv |
51 Matemáticas / Mathematics |
| topic |
51 Matemáticas / Mathematics Ricci flow blow-up convergence Flujo de Ricci explosión convergencia |
| dc.subject.proposal.spa.fl_str_mv |
Ricci flow blow-up convergence Flujo de Ricci explosión convergencia |
| description |
In this paper we study the Ricci flow on surfaces homeomorphic to a cylinder (that is, a product of the circle with a compact interval). We prove longtime existence results, results on the asymptotic behavior of the flow, and we report on an interesting phenomenon: convergence to constant curvature in the normalised flow, under certain assumptions on the initial data, cannot be exponential. |
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2017 |
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2017-07-01 |
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2019-07-03T02:07:08Z |
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2019-07-03T02:07:08Z |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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ISSN: 2357-4100 |
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https://repositorio.unal.edu.co/handle/unal/66433 |
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http://bdigital.unal.edu.co/67461/ |
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ISSN: 2357-4100 |
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spa |
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https://revistas.unal.edu.co/index.php/recolma/article/view/70903 |
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Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas Revista Colombiana de Matemáticas |
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Cortissoz, Jean C. and Murcia, Alexander (2017) The Ricci flow on a cylinder. Revista Colombiana de Matemáticas, 51 (2). pp. 241-257. ISSN 2357-4100 |
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Derechos reservados - Universidad Nacional de Colombia |
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http://purl.org/coar/access_right/c_abf2 |
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Atribución-NoComercial 4.0 Internacional |
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info:eu-repo/semantics/openAccess |
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Atribución-NoComercial 4.0 Internacional Derechos reservados - Universidad Nacional de Colombia http://creativecommons.org/licenses/by-nc/4.0/ http://purl.org/coar/access_right/c_abf2 |
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Universidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas - Sociedad Colombiana de Matemáticas |
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Universidad Nacional de Colombia |
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