Trudinger-Moser type inequalities with a symmetric conical metric and a symmetric potential

Let (M, g) be a closed Riemann surface, where the metric g has certain conical singularities at finite points. Suppose Gamma is a group with elements of isometrics acting on (M, g). In this paper, Trudinger-Moser inequalities involving Gamma and the operador Delta(g) + V are established, where Delta(g) denotes the Laplace-Beltrami operator associated to g and the potential V : M -> (0, infinity) belongs to a class of symmetric and continuous functions. Moreover, via the method of blow-up analysis, the corresponding extremals are also obtained. (C) 2022 Elsevier Ltd. All rights reserved.