## Energy distribution of harmonic 1-forms and Jacobians of Riemann surfaces with a short closed geodesic. (arXiv:1810.05259v1 [math.DG])

We study the energy distribution of harmonic 1-forms on a compact hyperbolic Riemann surface \$S\$ that has a small separating closed geodesic. The result is applied to the question how close the Jacobian torus of \$S\$ comes to a torus that splits. The aim is to answer this and related questions in terms of geometric data of \$S\$ such as its injectivity radius and the lengths of geodesics that form a homology basis. This is version 1 of an extended paper in which also non separating small geodesics are considered.查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 We study the energy distribution of harmonic 1-forms on a compact hyperbolic Riemann surface \$S\$ that has a small separating closed geodesic. The result is applied to the question how close the Jacobian torus of \$S\$ comes to a torus that splits. The aim is to answer this and related questions in terms of geometric data of \$S\$ such as its injectivity radius and the lengths of geodesics that form a homology basis. This is version 1 of an extended paper in which also non separating small geodesics are considered.
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