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The Spinor Representation of Minimal Surfaces
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The Spinor Representation of Minimal Surfaces
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The spinor representation is developed and used to investigate minimal surfaces in ${\bfR}^3$ with embedded planar ends. The moduli spaces of planar-ended minimal spheres and real projective planes are determined, and new families of minimal tori and Klein bottles are given. These surfaces compactify in $S^3$ to yield surfaces critical for the M\"obius invariant squared mean curvature functional $W$. On the other hand, all $W\!$-critical spheres and real projective planes arise this way. Thus we determine at the same time the moduli spaces of $W\!$-critical spheres and real projective planes via the spinor representation.
Forward citations
Cited by 2 Pith papers
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Neural Representation of Minimal Surfaces
Complex-valued neural nets for two holomorphic spinor functions yield minimal surfaces by construction and can be trained to match prescribed Plateau boundaries.
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Minimal surfaces with closed curvature lines
No complete non-orientable minimal surfaces of finite total curvature in R^3 with one end foliated by closed curvature lines exist.
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