On Minimal Annuli with a Straight Line Boundary

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Abstract

Shiffman proved that if a minimal annulus A in a slab is bounded by two convex Jordan curves contained respectively in the two boundary planes P and Q of the slab, then A intersects all parallel planes between P and Q in strictly convex curves. We generalize Shiffman's result to the case that A is bounded by a strictly convex C2 Jordan curve and a straight line. We show that in this case Shiffman's result is still true.

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