3 citations · 5 across the 4 of their papers we have counts for
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Gradient Shrinking Ricci Solitons and Modified Sectional Curvature
Xiaodong Cao, Ernani Ribeiro, Hosea Wondo
We investigate four-dimensional gradient shrinking Ricci solitons with positive modified sectional curvature. Our first main result shows that if the norm of the self-dual Weyl ten…
Integral and boundary estimates for critical metrics of the volume functional
Rafael Diógenes, Neilha Pinheiro, Ernani Ribeiro
In this article, we investigate the geometry of critical metrics of the volume functional on compact manifolds with boundary. We use the generalized Reilly's formula to derive new…
Estimates for Minimal Volume and Minimal Curvature on 4-dimensional compact manifolds
E. Costa, R. Diógenes, E. Ribeiro
In a remarkable article published in 1982, M. Gromov introduced the concept of minimal volume, namely, the minimal volume of a manifold is defined to be the greatest lower bo…
4-dimensional compact manifolds with nonnegative biorthogonal curvature
E. Costa, E. Ribeiro
The goal of this article is to study the pinching problem proposed by S.-T. Yau in 1990 replacing sectional curvature by one weaker condition on biorthogonal curvature. Moreover, w…