JournalsrmiVol. 30, No. 4pp. 1135–1148

Uniqueness of area minimizing surfaces for extreme curves

  • Baris Coskunuzer

    Koç University, Istanbul, Turkey
  • Tolga Etgü

    Koç University, Istanbul, Turkey
Uniqueness of area minimizing surfaces for extreme curves cover
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Abstract

Let MM be a compact, orientable, mean convex 33-manifold with boundary M\partial M. We show that the set of all simple closed curves in M\partial M which bound unique area minimizing disks in MM is dense in the space of simple closed curves in M\partial M which are nullhomotopic in MM. We also show that the set of all simple closed curves in M\partial M which bound unique absolutely area minimizing surfaces in MM is dense in the space of simple closed curves in M\partial M which are nullhomologous in MM.

Cite this article

Baris Coskunuzer, Tolga Etgü, Uniqueness of area minimizing surfaces for extreme curves. Rev. Mat. Iberoam. 30 (2014), no. 4, pp. 1135–1148

DOI 10.4171/RMI/810