Stability of Sobolev Inequalities - ICBS 2024

Explore a comprehensive lecture on the stability of Sobolev inequalities presented by Jun-cheng Wei at the ICBS2024 conference. Delve into Struwe's seminal work on the convergence of functions in the Sobolev space to sums of Aubin-Talenti bubbles. Examine the quantitative versions of Struwe's decomposition, including Ciraolo, Figalli, and Maggi's results for one bubble, and Figalli and Glaudo's dimensional-dependent estimates for multiple bubbles. Learn about the speaker's latest findings on sharp inequalities for the distance to the manifold of bubble sums in dimensions 6 and higher. Gain insights into related instability phenomena in harmonic map inequalities. This hour-long talk offers a deep dive into advanced mathematical concepts at the intersection of functional analysis and geometric analysis.