Mean curvature 1 surfaces in hyperbolic 3-space with low total curvature I

概要

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A complete surface of constant mean curvature $1$ (CMC-$1$) inhyperbolic $3$-space with constant curvature $-1$has two natural notions of ``total curvature''---one is the {\em total absolute curvature} which is the integral overthe surface of the absolute value of the Gaussian curvature,and the other is the {\em dual total absolute curvature} which is thetotal absolute curvature of the dual CMC-$1$ surface. In thispaper, we completely classify CMC-$1$ surfaces with dual totalabsolute curvature at most $4\pi$.Moreover, we give new examples and partially classify CMC-$1$surfaces with dual total absolute curvature at most $8\pi$.
広島大学の論文