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March 2022 Minimal planes in asymptotically flat three-manifolds
Laurent Mazet, Harold Rosenberg
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J. Differential Geom. 120(3): 533-556 (March 2022). DOI: 10.4310/jdg/1649953568

Abstract

In this paper, we improve a result by Chodosh and Ketover [2]. We prove that, in an asymptotically flat $3$-manifold $M$ that contains no closed minimal surfaces, fixing $q \in M$ and $V$ a $2$-plane in $T_q M$ 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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Laurent Mazet. Harold Rosenberg. "Minimal planes in asymptotically flat three-manifolds." J. Differential Geom. 120 (3) 533 - 556, March 2022. https://doi.org/10.4310/jdg/1649953568

Information

Received: 11 May 2018; Accepted: 11 March 2019; Published: March 2022
First available in Project Euclid: 15 April 2022

Digital Object Identifier: 10.4310/jdg/1649953568

Rights: Copyright © 2022 Lehigh University

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Vol.120 • No. 3 • March 2022
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