Abstract

MUNOZ MUNOZ, Sebastián  and  QUINTERO VELEZ, Alexander. Heat equation and stable minimal Morse functions on real and complex projective spaces. Rev.colomb.mat. [online]. 2017, vol.51, n.1, pp.71-82. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v51n1.66836.

Following similar results in (7) for flat tori and round spheres, in this paper is presented a proof of the fact that, for "arbitrary" initial conditions f 0 , the solution f t at time t of the heat equation on real or complex projective spaces eventually becomes (and remains) a minimal Morse function. Furthemore, it is shown that the solution becomes stable.

Keywords : Heat equation; Laplace-Beltrami operator; Minimal Morse function; Fubini-Study metric; Stable function.

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