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math.DG 1

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2026 1

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Geometric Reductions of the $G_2$-Hilbert Functional via Circle Actions

math.DG · 2026-05-03 · unverdicted · novelty 4.0

Under S1-invariant G2-structures with constant or varying fiber length, the unnormalized negative L2-gradient flow of the G2-Hilbert functional has only trivial stationary configurations: flat connections, scalar-flat base metrics, and constant fiber lengths.

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  • Geometric Reductions of the $G_2$-Hilbert Functional via Circle Actions math.DG · 2026-05-03 · unverdicted · none · ref 6

    Under S1-invariant G2-structures with constant or varying fiber length, the unnormalized negative L2-gradient flow of the G2-Hilbert functional has only trivial stationary configurations: flat connections, scalar-flat base metrics, and constant fiber lengths.