Convergence of the Yamabe flow for arbitrary initial energy

By S. Brendle. 2005

238 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/114de0f0ac30a26f68466c2f030f2b43c131b824

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Yanyan Li
2. A. Malchiodi
3. Lei Zhang
4. S. Brendle
5. Paul Yang
6. S. Chen
7. Jih-Hsin Cheng
8. L. Martinazzi

In Geometry and Topology

1. A. Malchiodi
2. Yanyan Li
3. S. Brendle
4. L. Martinazzi
5. Jih-Hsin Cheng
6. N. Šešum
7. Paul Yang
8. S. Chen

Citations in the corpus

• Convergence of the Yamabe flow in dimension 6 and higher (2007, background): “7, we discuss how the arguments in [ 5 ] can be adapted to prove convergence of the Yamabe flow.”
• An existence theorem for the Yamabe problem on manifolds with boundary (2009, methodology): “In order to show that the resuling testfunction has Yamabe energy less than Y (Sn+, ∂S n +), we make extensive use of techniques developed in [4] (see also [5], [6], [7]).”
• The classification of locally conformally flat Yamabe solitons (2011, background): “In [2] and [3] it has been showed that if 3 ≤ n ≤ 5 or if n ≥ 6 (in the latter case Brendle imposes that the metric is either locally conformally flat or he assumes a certain condition on the rate of vanishing of Weyl tensor at the points at which it”
• The Ricci-Bourguignon Flow (2015, unknown): “Moreover, by a suitable rescaling in time, when ρ is nonpositive, they can be seen as an interpolation between the Ricci flow and the Yamabe flow (see [Brendle 2005; Schwetlick and Struwe 2003; Ye 1994], for instance), obtained as a limit when ρ .”
• Compactness of solutions to the Yamabe problem (2004, background): “flows associated with the Yamabe problem and the Yamabe problem on manifolds with boundary, see for instance [93] , [86] and [ 20 ].”
• A Positive Mass Theorem in Three Dimensional Cauchy–Riemann Geometry (2013, background): “The positive mass theorem played a key role in other problems in conformal geometry, for example in the compactness of the Yamabe equation or the Yamabe flow, see [7], [8], [30].”
• A Note on Quasilinear Parabolic Equations on Manifolds (2010, background): “Our interest in having a handy proof of this result is related to geometric evolution problems, like for instance the Ricci flow, the mean curvature flow, the Willmore flow [7], the Q–curvature flow [9], the Yamabe flow [4, 11, 13], etc.”