On minimal surfaces bounded by two convex curves in parallel planes
نویسنده
چکیده
We prove that a compact minimal surface bounded by two closed convex curves in parallel planes close enough to each other must be topologically an annulus.
منابع مشابه
Minimal Surfaces Bounded by Convex Curves in Parallel Planes
In 1956 M. Shiffman [17] proved several beautiful theorems concerning the geometry of a minimal annulus A whose boundary consists of two closed convex curves in parallel planes P1, P2. The first theorem stated that the intersection of A with any plane P , between P1 and P2, is a convex Jordan curve. In particular it follows that A is embedded. He then used this convexity theorem to prove that e...
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تاریخ انتشار 2017