Finding Conformal and Isometric Immersions of Surfaces Article Swipe

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Albert Chern , Felix Knöppel , Franz Pedit , Ulrich Pinkall , Peter Schröder ·

YOU? · · 2019 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1901.09432 · OA: W4288621379

We introduce a family of variational functionals for spinor fields on a compact Riemann surface $M$ that can be used to find close-to-conformal immersions of $M$ into $\mathbb{R}^3$ in a prescribed regular homotopy class. Numerical experiments indicate that, by taking suitable limits, minimization of these functionals can also yield piecewise smooth isometric immersions of a prescribed Riemannian metric on $M$.