Entropías geométricas y monotonicidad bajo el flujo de Ricci.

Abstract

In this paper, we study the Perelman Wek entropy family proposed by Jun-Fang Li, its relationship with the Boltzmann-Shannon and Boltzmann-Nash-Shannon entropies. We analyze its monotonicity under a system of differential equations involving the Ricci flow. We constructed a new Perelman-type entropy family, and we make an analysis, similar to that made with the family Wek, taking in consideration the Shannon Entropy power in our calculations. In this sense, we exhibit important properties of the Ricci flow and its effects on curvature tensors. In addition, we study a couple of properties of the Perelman entropies F and W that are of vital importance for our purposes. Finally, we present the conclusions obtained in our study.