Abstract |
By using a simple topological argument, we show that the space of closed, orientable, codimension-1 submanifolds of Sn-1∞(Hn) which bound a unique
absolutely area minimizing hypersurface in Hn is dense in the space of closed, orientable, codimension-1 submanifolds of
Sn-1∞(Hn).
In particular, in dimension 3, we prove that the set of simple closed curves in
S2∞(Hn) bounding a unique absolutely area minimizing surface in
H3 is not only dense, but also a countable intersection of open dense subsets of the space of simple closed curves in
S2∞(Hn) with C0 topology.
We also show that the same is true for least area planes in H3. Moreover, we give some non-uniqueness results in dimension 3.
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