Showing papers on "Ricci decomposition published in 2019"
TL;DR: In this article, the authors extend Wei-Wylie's comparison results to the integral case and apply them to smooth metric measure spaces with their normalized integral smallness for Bakry-Emery Ricci tensor.
Abstract: We prove mean curvature and volume comparison estimates on smooth metric measure spaces when their integral Bakry–Emery Ricci tensor bounds, extending Wei–Wylie’s comparison results to the integral case. We also apply comparison results to get diameter estimates, eigenvalue estimates, and volume growth estimates on smooth metric measure spaces with their normalized integral smallness for Bakry–Emery Ricci tensor. These give generalizations of some work of Petersen–Wei, Aubry, Petersen–Sprouse, Yau and more.
11 citations
TL;DR: In this paper, it was shown that the symmetrized product of K-compatible tensors is a special Jordan algebra, i.e., the symmetric product of k-compatible symmetric tensors form a special algebra.
Abstract: Given the Riemann, or the Weyl, or a generalized curvature tensor K, a symmetric tensor $b_{ij}$ is named `compatible' with the curvature tensor if $b_i{}^m K_{jklm} + b_j{}^m K_{kilm} + b_k{}^m K_{ijlm} = 0$. Amongst showing known and new properties, we prove that they form a special Jordan algebra, i.e. the symmetrized product of K-compatible tensors is K-compatible.
7 citations