Trudinger–Moser type inequalities with a symmetric conical metric and a symmetric potential. (October 2022) - de Souza, Manassés X.
Abstract: Let ( M, g ) be a closed Riemann surface, where the metric g has certain conical singularities at finite points. Suppose Γ is a group with elements of isometries acting on ( M, g ) . In this paper, Trudinger–Moser inequalities involving Γ and the operador Δ g + V are established, where Δ g denotes the Laplace–Beltrami operator associated to g and the potential V : M → ( 0, ∞ ) belongs to a class of symmetric and continuous functions. Moreover, via the method of blow-up analysis, the corresponding extremals are also obtained.