Revista Matemática Iberoamericana


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Volume 30, Issue 4, 2014, pp. 1135–1148
DOI: 10.4171/RMI/810

Published online: 2014-12-15

Uniqueness of area minimizing surfaces for extreme curves

Baris Coskunuzer[1] and Tolga Etgü[2]

(1) Koç University, Istanbul, Turkey
(2) Koç University, Istanbul, Turkey

Let $M$ be a compact, orientable, mean convex $3$-manifold with boundary $\partial M$. We show that the set of all simple closed curves in $\partial M$ which bound unique area minimizing disks in $M$ is dense in the space of simple closed curves in $\partial M$ which are nullhomotopic in $M$. We also show that the set of all simple closed curves in $\partial M$ which bound unique absolutely area minimizing surfaces in $M$ is dense in the space of simple closed curves in $\partial M$ which are nullhomologous in $M$.

Keywords: Plateau problem, area minimizing surfaces, minimal surfaces, mean convex 3-manifolds, uniqueness

Coskunuzer Baris, Etgü Tolga: Uniqueness of area minimizing surfaces for extreme curves. Rev. Mat. Iberoamericana 30 (2014), 1135-1148. doi: 10.4171/RMI/810