Abstract

CADAVID MORENO, Carlos  and  VELEZ CAICEDO, Juan Diego. A Remark on the Heat Equation and Minimal Morse Functions on Tori and Spheres. ing.cienc. [online]. 2013, vol.9, n.17, pp.11-20. ISSN 1794-9165.

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 f₀, the solution to f /t = Δ_gf, 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.

Keywords : morse function; heat equation.

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