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
| Summary: | 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. |
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