Uniqueness of area minimizing surfaces for extreme curves

  • Baris Coskunuzer

    Koç University, Istanbul, Turkey
  • Tolga Etgü

    Koç University, Istanbul, Turkey

Abstract

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

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