# Stability of Sobolev and Harmonic Map Inequalities

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Juncheng Wei, The University of British Columbia

Online Talk

In this talk, I will discuss our recent results on stability of Sobolev inequalities and Harmonic Map Inequalities. For Sobolev inequality we obtain the sharp estimates of the deficiency of $u$ and sum of Talenti bubbles in terms of the $H^{-1}$ norm of the Yamabe equation $\Delta u + u^{\frac{n+2}{n-2}}$. For Harmonic Maps Inequalities, we show that a striking dichotomy in stability between degree one and higher degree maps.