Recent progress on the Yamabe problem
S. Brendle, F.C. Marques
TL;DR
This paper surveys recent advances in understanding the Yamabe problem, focusing on compactness results, non-compactness phenomena, and the asymptotic behavior of the Yamabe flow, highlighting ongoing conjectures and open questions.
Contribution
It provides a comprehensive overview of recent progress on the Yamabe problem, emphasizing new results and conjectures in the field.
Findings
Summary of compactness and non-compactness results for the Yamabe equation
Discussion of Hamilton's conjecture on Yamabe flow behavior
Identification of open problems and future research directions
Abstract
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 parabolic Yamabe flow.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Geometric Analysis and Curvature Flows · Geometric and Algebraic Topology