We introduce a natural extension of the concept of gradient Ricci soliton: the Ricci almost
soliton. We provide existence and rigidity results, we deduce a-priori curvature estimates …

In 1967, studying the possibility of minimally immersing complete submanifolds into
Euclidean cones, Omori [210] introduced an important analytical tool nowadays called the …

We call a metric quasi-Einstein if the m-Bakry–Emery Ricci tensor is a constant multiple of
the metric tensor. This is a generalization of Einstein metrics, it contains gradient Ricci …

We define a gradient Ricci soliton to be rigid if it is a flat bundle N× Γ ℝ k where N is Einstein.
It is known that not all gradient solitons are rigid. Here we offer several natural conditions on …

We show that the only shrinking gradient solitons with vanishing Weyl tensor and Ricci
tensor satisfying a weak integral condition are quotients of the standard ones S n, S n− 1× ℝ …

The main aim of this book is to present recent developments of comparison geometry and
geometric analysis on Finsler manifolds in an accessible way to students and researchers …

In the first part of the paper we derive integral curvature estimates for complete gradient
shrinking Ricci solitons. Our results and the recent work in M. Fernandez-Lopez and E …

The aim of this paper is to find some equations of structure for almost Ricci solitons which
generalize the equivalent for Ricci solitons. As a consequence of these equations we derive …

In this paper we show how techniques coming from stochastic analysis, such as stochastic
completeness (in the form of the weak maximum principle at infinity), parabolicity and L p …

In this article, we classify n-dimensional (n≥ 4) complete Bach-flat gradient shrinking Ricci
solitons. More precisely, we prove that any 4-dimensional Bach-flat gradient shrinking Ricci …