Asymptotics of the Gaussian Curvatures of the Canonical Metric on the Surface
نویسنده
چکیده
We study the canonical metric on a compact Riemann surface of genus at least two. This natural metric is the pullback, via the period map, from the Euclidean metric on the Jacobian variety of the surface. While it is known that the canonical metric is of nonpositive curvature, we show that its Gaussian curvatures are not bounded away from zero nor negative infinity when the surface is close to the compactification divisor of Riemann’s moduli space.
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تاریخ انتشار 2006