MathDB3 problems
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Existence of minimally screw-symmetric minimal surfaces
Screw-only symmetry conjecture. There exist SMIMS which are only symmetric with respect to screw motions.
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Multiplicity of genus 2 helicoids
Multiplicity conjecture. There exist multiple translation-invariant genus 2 helicoids and multiple genus 2 helicoids.
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Uniqueness of minimal surfaces asymptotic to helicoids
Uniqueness conjecture. These surfaces are the unique minimal surfaces with these properties.