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Given a smooth closed connected curve $\gamma$ in $\mathbb R^3$, is there an immersed surface $S$ with boundary (topologically necessarily a disk), such that its Gaussian curvature is equal to zero and $\partial S=\gamma$?

Given a smooth closed connected curve $\gamma$ in $\mathbb R^3$, is there an immersed surface $S$ with boundary (topologically necessarily a disk), such that its Gaussian curvature is equal to zero and $\partial S=\gamma$?

Given a smooth closed connected curve $\gamma$ in $\mathbb R^3$, is there an immersed surface $S$ with boundary, such that its Gaussian curvature is equal to zero and $\partial S=\gamma$?

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Spanning curves by flat surfaces

Given a smooth closed connected curve $\gamma$ in $\mathbb R^3$, is there an immersed surface $S$ with boundary (topologically necessarily a disk), such that its Gaussian curvature is equal to zero and $\partial S=\gamma$?