A Remark on the Heat Equation and Minimal Morse Functions on Tori and Spheres

Ingeniería y Ciencia

Cadavid Moreno, Carlos²  Vélez Caicedo, Juan Diego¹ 

[1] Universidad Nacional de Colombia, Medellín, Colombia;Universidad EAFIT, Medellín, Colombia

关键词: morse function;    heat equation;   

DOI  :  

学科分类：工程和技术（综合）

来源: Universidad E A F I T

【 摘 要 】

Let (M, g) be a compact, connected riemannian manifold that is homogeneous, i.e. each pair of points p, qM 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 f0, the solution to f /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.

【 授权许可】

Unknown