On the conformal scalar curvature equation and related problems
S. Brendle
TL;DR
This paper reviews recent advances in understanding the Yamabe equation, focusing on compactness, non-compactness, and the asymptotic behavior of the Yamabe flow, which are key to geometric analysis.
Contribution
It provides a comprehensive review of recent results on the Yamabe equation and flow, highlighting new insights into their compactness properties and asymptotic behavior.
Findings
Summary of recent compactness results for the Yamabe equation
Discussion of non-compactness phenomena in Yamabe problems
Analysis of the asymptotic behavior of the Yamabe flow
Abstract
We review recent compactness and non-compactness results for the Yamabe equation. We also discuss the asymptotic behavior of the parabolic Yamabe flow.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Geometry and complex manifolds