Heat equation and stable minimal Morse functions on real and complex projective spaces
Abstract
Following similar results in arXiv:1301.5934 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. Furthermore, it is shown that the solution becomes stable.
 Publication:

arXiv eprints
 Pub Date:
 March 2017
 DOI:
 10.48550/arXiv.1703.01105
 arXiv:
 arXiv:1703.01105
 Bibcode:
 2017arXiv170301105M
 Keywords:

 Mathematics  Differential Geometry;
 Mathematical Physics
 EPrint:
 8 pages