51 citations · 88 across the 5 of their papers we have counts for
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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…
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…
Deformations of the hemisphere that increase scalar curvature
S. Brendle, F. C. Marques, A. Neves
Consider a compact Riemannian manifold M of dimension n whose boundary \partial M is totally geodesic and is isometric to the standard sphere S^{n-1}. A natural conjecture of Min-O…
Blow-up phenomena for the Yamabe equation II
S. Brendle, F. C. Marques
Let n be an integer such that 25 \leq n \leq 51. We construct a smooth metric g on S^n with the property that the set of constant scalar curvature metrics in the conformal class of…
A priori estimates for the Yamabe problem in the non-locally conformally flat case
Fernando C. Marques
Given a compact Riemannian manifold, with positive Yamabe quotient, not conformally diffeomorphic to the standard sphere, we prove a priori estimates for solutions to the Yamabe pr…