In this paper, the idea of the Ricci flow is introduced and its significance and importance to related problems in mathematics had been discussed. Several functionals are defined and their behavior is studied under Ricci flow. A unique minimizer is shown to exist for one of the functionals. This functional evaluated at the minimizer is strictly increasing. The results for the first functional considered are extended to manifold with boundary. Finally, two physically motivated examples are presented.
Bracken, Paul. "Monotonicity properties of functionals under Ricci flow on manifolds without and with boundary." International Journal of Geometric Methods in Modern Physics 19.9 (2022): 2250137-262. https://doi.org/10.1142/S0219887822501377
International Journal of Geometric Methods in Modern Physics