Wang, Ai Nung On convexity of level curves. (English) Zbl 0697.53016 Chin. J. Math. 17, No. 4, 307-308 (1989). Let M be a minimal surface in space bounded by two plane curves \(C_ 1\), \(C_ 2\) lying in parallel planes. If \(C_ 1\), \(C_ 2\) are convex curves, then the intersection of M by a plane parallel to the planes of \(C_ 1\), \(C_ 2\) is again a convex curve. That assertion has been established by M. Shiffman [Ann. Math., II. Ser. 63, 77-90 (1956; Zbl 0070.168)]. In this note the author shows that, by constructing a counterexample, the above assertion is false for surfaces with constant non-zero mean curvature. Reviewer: T.Hasanis MSC: 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature 53A05 Surfaces in Euclidean and related spaces Keywords:minimal surface; convex curve; constant non-zero mean curvature Citations:Zbl 0070.168 PDFBibTeX XMLCite \textit{A. N. Wang}, Chin. J. Math. 17, No. 4, 307--308 (1989; Zbl 0697.53016)