Area bounds for minimal surfaces that pass through a prescribed point in a ball

S. Brendle; P. K. Hung

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arXiv · 1607.04631

Area bounds for minimal surfaces that pass through a prescribed point in a ball

S. Brendle·P. K. Hung

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Abstract

Let $Σ$ be a $k$-dimensional minimal submanifold in the $n$-dimensional unit ball $B^n$ which passes through a point $y \in B^n$ and satisfies $\partial Σ\subset \partial B^n$. We show that the $k$-dimensional area of $Σ$ is bounded from below by $|B^k| \, (1-|y|^2)^{\frac{k}{2}}$. This settles a question left open by the work of Alexander and Osserman in 1973.

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BibTeX RIS

S. Brendle, P. K. Hung. 2017-01-27. Area bounds for minimal surfaces that pass through a prescribed point in a ball. https://arxiv.org/abs/1607.04631

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