Document Zbl 0747.53047

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Intersections of least area surfaces. (English) Zbl 0747.53047

Pac. J. Math. 152, No. 1, 119-123 (1992).

The author constructs a properly embedded complete plane \(P\) of least area in hyperbolic 3-space (i.e. any subdisc of \(P\) has least area among discs with the same boundary) together with a smooth Jordan curve \(\gamma\) disjoint from \(P\), such that any least area disc spanning \(\gamma\) must intersect \(P\). Since such an intersection is topologically not necessary, this example shows the limitations of the philosophy saying that least area surface intersect least.

Reviewer: F.Tomi (Heidelberg)

Cited in 2 Documents

MSC:

53C42

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)

Keywords:

intersections of minimal surfaces; hyperbolic 3-space

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