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Finding Conformal and Isometric Immersions of Surfaces

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abstract

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 $M$.

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gr-qc 1

years

2026 1

verdicts

UNVERDICTED 1

representative citing papers

Spacetime triple wormhole

gr-qc · 2026-05-25 · unverdicted · novelty 5.0

A 3-neck wormhole metric obtained via spherical inversion of a 3-torus is asserted to be an exact non-vacuum solution of Einstein's field equations with diagonal Ricci and stress-energy tensors.

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  • Spacetime triple wormhole gr-qc · 2026-05-25 · unverdicted · none · ref 29 · internal anchor

    A 3-neck wormhole metric obtained via spherical inversion of a 3-torus is asserted to be an exact non-vacuum solution of Einstein's field equations with diagonal Ricci and stress-energy tensors.