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Asymptotically flat three-manifolds contain minimal planes

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Let $(M,g)$ be an asymptotically flat $3$-manifold containing no closed embedded minimal surfaces. We prove that for every point $p\in M$ there exists a complete properly embedded minimal plane in… Click to show full abstract

Let $(M,g)$ be an asymptotically flat $3$-manifold containing no closed embedded minimal surfaces. We prove that for every point $p\in M$ there exists a complete properly embedded minimal plane in $M$ containing $p$.

Keywords: manifolds contain; contain minimal; minimal planes; three manifolds; asymptotically flat; flat three

Journal Title: Advances in Mathematics
Year Published: 2018

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