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“Large” conformal metrics of prescribed Gauss curvature on surfaces of higher genus

“Large” conformal metrics of prescribed Gauss curvature on surfaces of higher genus

Let (M,g_0) be a closed Riemann surface (M,g_0) of genus \gamma(M)>1 and let f_0 be a smooth, non-constant function with \mathrm {max}_{p\in M}f_0(p)=0 , all of whose maximum points are non-degenerate. As shown in [12] for sufficiently small \lambda>0 there exist at least two distinct conformal metrics g_{\lambda}=e^{2u_{\lambda}}g_0 , g^{\lambda}=e^{2u^{\lambda}}g_0 …