Minimal planes in asymptotically flat three-manifolds

Minimal planes in asymptotically flat three-manifolds

In this paper, we improve a result by Chodosh and Ketover. We prove that, in an asymptotically flat $3$-manifold $M$ that contains no closed minimal surfaces, fixing $q\in M$ and a $2$-plane $V$ in $T_qM$ there is a properly embedded minimal plane $\Sigma$ in $M$ such that $q\in\Sigma$ and $T_q\Sigm...

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Veröffentlicht in:Journal of Differential Geometry 2022-03, Vol.120 (3)
Hauptverfasser: Mazet, Laurent, Rosenberg, Harold
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Sprache:eng
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Differential Geometry
Mathematics
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description In this paper, we improve a result by Chodosh and Ketover. We prove that, in an asymptotically flat $3$-manifold $M$ that contains no closed minimal surfaces, fixing $q\in M$ and a $2$-plane $V$ in $T_qM$ there is a properly embedded minimal plane $\Sigma$ in $M$ such that $q\in\Sigma$ and $T_q\Sigma=V$. We also prove that fixing three points in $M$ there is a properly embedded minimal plane passing through these three points.
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title Minimal planes in asymptotically flat three-manifolds
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