Abstract
We show that highly twisted minimal strips can undergo a nonsingular transition, unlike the singular transitions seen in the Möbius strip and the catenoid. If the strip is nonorientable, this transition is topologically frustrated, and the resulting surface contains a helicoidal defect. Through a controlled analytic approximation, the system can be mapped onto a scalar ϕ^{4} theory on a nonorientable line bundle over the circle, where the defect becomes a topologically protected kink soliton or domain wall, thus establishing their existence in minimal surfaces. Demonstrations with soap films confirm these results and show how the position of the defect can be controlled through boundary deformation.
Highlights
Minimal surfaces, critical points of the area functional, are geometric motifs that appear throughout physics
We show that highly twisted minimal strips can undergo a nonsingular transition, unlike the singular transitions seen in the Möbius strip and the catenoid
Through a controlled analytic approximation, the system can be mapped onto a scalar φ4 theory on a nonorientable line bundle over the circle, where the defect becomes a topologically protected kink soliton or domain wall, establishing their existence in minimal surfaces
Summary
Critical points of the area functional, are geometric motifs that appear throughout physics. If the strip is nonorientable, this transition is topologically frustrated, and the resulting surface contains a helicoidal defect.
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