Thread-wire surfaces: Near-wire minimizers and topological finiteness

Abstract

Alt’s thread problem asks for least-area surfaces bounding a fixed “wire” curve and a movable “thread” curve of length L. We conjecture that if the wire has finitely many maxima of curvature, then its Alt minimizers have finitely many surface components. We show that this conjecture reduces to controlling near-wire minimizers, and thus begin a three paper… (More)

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