Spectral convergence of conformally immmersed surfaces with bounded mean curvature (Q1407745)

The authors [Tôhoku Math. J., II. Ser. 46, No. 2, 147--179 (1994; Zbl 0814.53035)] introduced the spectral distance between compact connected Riemannian manifolds by using their heat kernels and studied its basic properties. In the paper under review, the authors deal with a family of conformally immersed surfaces with bounded mean curvature and apply the theory of bubble tree convergence to such a family, in order to study its spectral convergence. The spectral limit is described. In this respect, the \(\varepsilon\)-compactness of a branched conformal immersion and removable singularity are studied.