2025/08/27 by Ghosh, Monideep, Karmakar, Debabrata · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2508.19930
In this work, we focus on a recent variant of the Trudinger-Moser-Onofri inequality introduced by S. Y. Alice Chang and Changfeng Gui \citeCG-2023: α∫_\mathbbS2|∇_\mathbbS2u|2 \rm dω+2 ∫_\mathbbS2 u \rm dω-(1)/(2)ln[(∫_\mathbbs2e2u\rm dω)2-∑i=13(∫_\mathbbs2ωi e2u\rm d ω)2] ≥ 0 holds on H1(\mathbbS2) if and only if α≥ (2)/(3). In this regime, the infimum is attained only by trivial functions when α> (2)/(3), whereas for the critical value α= (2)/(3) nontrivial extremals exist, and Chang-Gui further provided a complete classification of such solutions. Building upon their result, we found a nice conformal invariance of the associated functional. Exploiting this invariance, we were able to characterize the full family of extremals in terms of conformal maps of \mathbbS2 and, moreover, establish a sharp quantitative stability result in the gradient norm.