Boundary torsion and convex caps of locally convex surfaces. (English) Zbl 1381.53017

The author investigates an open question by Yau, regarding when a closed curve in three-space bounds a disk of positive curvature. Following up on prior conjecture, he finds that the curve must have at least four vertices, establishing a new requirement for the existence of such curves. The majority of the paper is dedicated to proving this result. However, the last section contains a collection of examples to cast some relief on the proof, showing applications to real curves.


53A05 Surfaces in Euclidean and related spaces
53A04 Curves in Euclidean and related spaces
57R40 Embeddings in differential topology
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