Uniform weak-field and small-flux asymptotics for exterior magnetic Steklov operators

Henry Zweiman · September 16, 2026 · P51 · Version 1.0

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The paper gives a uniform operator expansion for planar exterior magnetic Steklov problems as field and scalar mass vanish, including the transition across integral Aharonov–Bohm flux. It derives a universal ground-state crossover, a signed-flux asymmetry and a second-order geometric gap. Every fixed smooth simply connected nondisk is strictly below the equal-perimeter disk in an obstacle-dependent small-parameter neighborhood, without symmetry or convexity assumptions.

The scalar capacity expansion, classical circle spectra, Kummer identity, conformal covariance and boundary calculus are credited prior work. Thresholds depend on the obstacle; no full-field-range theorem or independent flux-vector theorem is claimed. Exact source-access limits are disclosed in the assessment.

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