77 citations · 178 across the 21 of their papers we have counts for
6 papers · 1 filter
Recent progress on the Yamabe problem
S. Brendle, F. C. Marques
We give a survey of various compactness and non-compactness results for the Yamabe equation. We also discuss a conjecture of Hamilton concerning the asymptotic behavior of the para…
Uniqueness of gradient Ricci solitons
S. Brendle
We show that a three-dimensional steady gradient Ricci soliton which is asymptotic to the Bryant soliton in a suitable sense must be isometric to the Bryant soliton.
Rigidity phenomena involving scalar curvature
S. Brendle
We give a survey of various rigidity results involving scalar curvature. Many of these results are inspired by the positive mass theorem in general relativity. In particular, we di…
Scalar curvature rigidity of geodesic balls in S^n
S. Brendle, F. C. Marques
In this paper, we prove a scalar curvature rigidity result for geodesic balls in S^n. This result contrasts sharply with the recent counterexamples to Min-Oo's conjecture for the h…
Einstein metrics and preserved curvature conditions for the Ricci flow
S. Brendle
Let C be a cone in the space of algebraic curvature tensors. Moreover, let (M,g) be a compact Einstein manifold with the property that the curvature tensor of (M,g) lies in the con…
Curvature, sphere theorems, and the Ricci flow
S. Brendle, R. M. Schoen
This is a survey paper focusing on the interplay between the curvature and topology of a Riemannian manifold. The first part of the paper provides a background discussion, aimed at…