Gromov-Hausdorff convergence theory of surfaces

In this paper, we use the viewpoint of Gromov-Haustorff convergence to give some new comprehension of well known theorem,it is Huber's classification theorem\cite{Huber}\cite{MS}for complete Riemannian surfaces immersed in $\mathbb{R}^n$ with finite total curvature( $\int_Σ|A|^2<+\infty$) it depend heavily on Müller and Šverák's Hardy-estimate\cite{MS} for the curvature form of surfaces immersed in $\mathbb{R}^n$ with finite total curvature.

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