Area bounds for minimal surfaces in geodesic ball of hyperbolic space

Jingze Zhu

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arXiv · 1612.02722

Area bounds for minimal surfaces in geodesic ball of hyperbolic space

Jingze Zhu

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Abstract

In hyperbolic space $H^n$ we set a geodesic ball of radius $\rho$. Consider a $k$ dimensional minimal submanifold passing through the origin of the geodesic ball with boundary lies on the boundary of that geodesic ball. We prove that its area is no less than the totally geodesic $k$ dimensional submanifold passing through the origin in that geodesic ball. This is a partial generalization of the corresponding problem in $R^n$.

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BibTeX RIS

Jingze Zhu. 2016-12-08. Area bounds for minimal surfaces in geodesic ball of hyperbolic space. https://arxiv.org/abs/1612.02722

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