A Remark on the Heat Equation and Minimal Morse Functions on Tori and Spheres
Let (M, g) be a compact, connected riemannian manifold that is homogeneous, i.e. each pair of points p, q ∈ M have isometric neighborhoods. This paper is a first step towards an understanding of the extent to which it is true that for each "generic" initial condition ff/∂t = Δgf, f(⋅, 0) =...
- Autores:
-
Cadavid, Carlos
Vélez Caicedo, Juan Diego
- Tipo de recurso:
- Fecha de publicación:
- 2013
- Institución:
- Universidad EAFIT
- Repositorio:
- Repositorio EAFIT
- Idioma:
- eng
- OAI Identifier:
- oai:repository.eafit.edu.co:10784/14408
- Acceso en línea:
- http://hdl.handle.net/10784/14408
- Palabra clave:
- Morse Function
Heat Equation
Función Morse
Ecuación De Calor
- Rights
- License
- Copyright (c) 2013 Carlos Cadavid, Juan Diego Vélez Caicedo
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Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees2013-03-222019-11-22T17:02:38Z2013-03-222019-11-22T17:02:38Z2256-43141794-9165http://hdl.handle.net/10784/1440810.17230/ingciecia.9.17.1Let (M, g) be a compact, connected riemannian manifold that is homogeneous, i.e. each pair of points p, q ∈ M have isometric neighborhoods. This paper is a first step towards an understanding of the extent to which it is true that for each "generic" initial condition ff/∂t = Δgf, f(⋅, 0) = f0 is such that for sufficiently large t, f(⋅ t) is a minimal Morse function, i.e., a Morse function whose total number of critical points is the minimal possible on M. In this paper we show that this is true for flat tori and round spheres in all dimensions.Sea (M, g) una variedad riemanniana compacta y conectada que es homogénea, es decir, cada par de puntos p, q ∈ M tiene vecindades isométricas. Este documento es un primer paso hacia una comprensión de la medida en que es cierto que para cada condición inicial "genérica" ff / ∂t = Δgf, f (⋅, 0) = f0 es tal que para t suficientemente grande, f ( ⋅ t) es una función Morse mínima, es decir, una función Morse cuyo número total de puntos críticos es el mínimo posible en M. En este artículo mostramos que esto es cierto para toros planos y esferas redondas en todas las dimensiones.application/pdfengUniversidad EAFIThttp://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/1839http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/1839Copyright (c) 2013 Carlos Cadavid, Juan Diego Vélez CaicedoAcceso abiertohttp://purl.org/coar/access_right/c_abf2instname:Universidad EAFITreponame:Repositorio Institucional Universidad EAFITIngeniería y Ciencia; Vol 9, No 17 (2013)A Remark on the Heat Equation and Minimal Morse Functions on Tori and SpheresUna nota acerca de la ecuación del calor y funciones de Morse minimales en toros y esferasarticleinfo:eu-repo/semantics/articlepublishedVersioninfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Morse FunctionHeat EquationFunción MorseEcuación De CalorCadavid, Carlos738f394c-0933-4d83-982c-62e076584103-1Vélez Caicedo, Juan Diego84f3b6cb-3d98-4f68-a998-de4025bfc80b-1Universidad EAFITUniversidad Nacional de ColombiaIngeniería y Ciencia9171120ing.cienc.THUMBNAILminaitura-ig_Mesa de trabajo 1.jpgminaitura-ig_Mesa de trabajo 1.jpgimage/jpeg265796https://repository.eafit.edu.co/bitstreams/5286fbce-16d3-4dd5-9aa4-9cbb6afb64e1/downloadda9b21a5c7e00c7f1127cef8e97035e0MD51ORIGINAL1.pdf1.pdfTexto completo PDFapplication/pdf475234https://repository.eafit.edu.co/bitstreams/4749131d-616e-48e2-86ae-1b8a9cebb31f/downloadecf6082498932a89f3c92a04e050e5ebMD52articulo.htmlarticulo.htmlTexto completo HTMLtext/html374https://repository.eafit.edu.co/bitstreams/942e6aec-faf5-42f9-91df-2b9d8c55c7f4/download8fd186238aacdfbd9b0a5fec35c8f24fMD5310784/14408oai:repository.eafit.edu.co:10784/144082024-12-04 11:48:02.413open.accesshttps://repository.eafit.edu.coRepositorio Institucional Universidad EAFITrepositorio@eafit.edu.co |
| dc.title.eng.fl_str_mv |
A Remark on the Heat Equation and Minimal Morse Functions on Tori and Spheres |
| dc.title.spa.fl_str_mv |
Una nota acerca de la ecuación del calor y funciones de Morse minimales en toros y esferas |
| title |
A Remark on the Heat Equation and Minimal Morse Functions on Tori and Spheres |
| spellingShingle |
A Remark on the Heat Equation and Minimal Morse Functions on Tori and Spheres Morse Function Heat Equation Función Morse Ecuación De Calor |
| title_short |
A Remark on the Heat Equation and Minimal Morse Functions on Tori and Spheres |
| title_full |
A Remark on the Heat Equation and Minimal Morse Functions on Tori and Spheres |
| title_fullStr |
A Remark on the Heat Equation and Minimal Morse Functions on Tori and Spheres |
| title_full_unstemmed |
A Remark on the Heat Equation and Minimal Morse Functions on Tori and Spheres |
| title_sort |
A Remark on the Heat Equation and Minimal Morse Functions on Tori and Spheres |
| dc.creator.fl_str_mv |
Cadavid, Carlos Vélez Caicedo, Juan Diego |
| dc.contributor.author.spa.fl_str_mv |
Cadavid, Carlos Vélez Caicedo, Juan Diego |
| dc.contributor.affiliation.spa.fl_str_mv |
Universidad EAFIT Universidad Nacional de Colombia |
| dc.subject.keyword.eng.fl_str_mv |
Morse Function Heat Equation |
| topic |
Morse Function Heat Equation Función Morse Ecuación De Calor |
| dc.subject.keyword.spa.fl_str_mv |
Función Morse Ecuación De Calor |
| description |
Let (M, g) be a compact, connected riemannian manifold that is homogeneous, i.e. each pair of points p, q ∈ M have isometric neighborhoods. This paper is a first step towards an understanding of the extent to which it is true that for each "generic" initial condition ff/∂t = Δgf, f(⋅, 0) = f0 is such that for sufficiently large t, f(⋅ t) is a minimal Morse function, i.e., a Morse function whose total number of critical points is the minimal possible on M. In this paper we show that this is true for flat tori and round spheres in all dimensions. |
| publishDate |
2013 |
| dc.date.issued.none.fl_str_mv |
2013-03-22 |
| dc.date.available.none.fl_str_mv |
2019-11-22T17:02:38Z |
| dc.date.accessioned.none.fl_str_mv |
2019-11-22T17:02:38Z |
| dc.date.none.fl_str_mv |
2013-03-22 |
| dc.type.eng.fl_str_mv |
article info:eu-repo/semantics/article publishedVersion info:eu-repo/semantics/publishedVersion |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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http://purl.org/coar/resource_type/c_6501 http://purl.org/coar/resource_type/c_2df8fbb1 |
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Artículo |
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publishedVersion |
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2256-4314 1794-9165 |
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http://hdl.handle.net/10784/14408 |
| dc.identifier.doi.none.fl_str_mv |
10.17230/ingciecia.9.17.1 |
| identifier_str_mv |
2256-4314 1794-9165 10.17230/ingciecia.9.17.1 |
| url |
http://hdl.handle.net/10784/14408 |
| dc.language.iso.eng.fl_str_mv |
eng |
| language |
eng |
| dc.relation.isversionof.none.fl_str_mv |
http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/1839 |
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http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/1839 |
| dc.rights.eng.fl_str_mv |
Copyright (c) 2013 Carlos Cadavid, Juan Diego Vélez Caicedo |
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http://purl.org/coar/access_right/c_abf2 |
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Acceso abierto |
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Copyright (c) 2013 Carlos Cadavid, Juan Diego Vélez Caicedo Acceso abierto http://purl.org/coar/access_right/c_abf2 |
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application/pdf |
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Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees |
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Universidad EAFIT |
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instname:Universidad EAFIT reponame:Repositorio Institucional Universidad EAFIT |
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Ingeniería y Ciencia; Vol 9, No 17 (2013) |
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