Generalized L-geodesic and monotonicity of the generalized reduced volume in the Ricci flow
Generalized L-geodesic and monotonicity of the generalized reduced volume in the Ricci flow
Suppose $M$ is a complete n-dimensional manifold, $n\ge 2$, with a metric $\overline{g}_{ij}(x,t)$ that evolves by the Ricci flow $\partial_t \overline{g}_{ij}=-2\overline{R}_{ij}$ in $M\times (0,T)$. For any $0<p<1$, $(p_0,t_0)\in M\times (0,T)$, $q\in M$, we define the $\mathcal{L}_p$-length between $p_0$ and $q$, $\mathcal{L}_p$-geodesic, the generalized reduced distance $l_p$ and the generalized reduced …