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math.AP2026
A priori Dirichlet energy bounds for positive Trudinger--Moser critical points on simply connected planar domains
Hongtao Hu, Qiaoran Wu, Wenming Zou
\noindent Let \(\Om\subset\R^2\) be a smooth bounded simply connected domain. We prove that all positive solutions of \(-Δu=θue^{u^2}\), with \(θ>0\) and zero Dirichlet boundary da…
math.AP2026
Sharp Harmonic-Mean Bounds for Neumann Eigenvalues on Riemannian Surfaces and Counterexamples to Geodesic Ball Optimality on Higher-Dimensional Spheres
Hongtao Hu, Meiqi Liu, Qiaoran Wu +1
Let be a bounded simply connected Lipschitz domain with conformal metric , where is positive in the interior and may te…