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)...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Universidad EAFIT
2013-03-01
|
| Series: | Ingeniería y Ciencia |
| Subjects: | |
| Online Access: | http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/1839 |
| id |
doaj-a171732c341c494cbf2bdcd020fd0146 |
|---|---|
| record_format |
Article |
| spelling |
doaj-a171732c341c494cbf2bdcd020fd01462020-11-24T22:25:16ZengUniversidad EAFITIngeniería y Ciencia1794-91652256-43142013-03-0191710.17230/ingciecia.9.17.11839A Remark on the Heat Equation and Minimal Morse Functions on Tori and SpheresCarlos Cadavid0Juan Diego Vélez Caicedo1Universidad EAFITUniversidad Nacional de Colombia 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. MSC: 53C, 53A http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/1839morse functionheat equation |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Carlos Cadavid Juan Diego Vélez Caicedo |
| spellingShingle |
Carlos Cadavid Juan Diego Vélez Caicedo A Remark on the Heat Equation and Minimal Morse Functions on Tori and Spheres Ingeniería y Ciencia morse function heat equation |
| author_facet |
Carlos Cadavid Juan Diego Vélez Caicedo |
| author_sort |
Carlos Cadavid |
| title |
A Remark on the Heat Equation and Minimal Morse Functions on Tori and Spheres |
| 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 |
remark on the heat equation and minimal morse functions on tori and spheres |
| publisher |
Universidad EAFIT |
| series |
Ingeniería y Ciencia |
| issn |
1794-9165 2256-4314 |
| publishDate |
2013-03-01 |
| 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.
MSC: 53C, 53A
|
| topic |
morse function heat equation |
| url |
http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/1839 |
| work_keys_str_mv |
AT carloscadavid aremarkontheheatequationandminimalmorsefunctionsontoriandspheres AT juandiegovelezcaicedo aremarkontheheatequationandminimalmorsefunctionsontoriandspheres AT carloscadavid remarkontheheatequationandminimalmorsefunctionsontoriandspheres AT juandiegovelezcaicedo remarkontheheatequationandminimalmorsefunctionsontoriandspheres |
| _version_ |
1725758561169965056 |