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  1. Locating Quintic Obstructions in the Riemann Theta Product: A certified transition and minimum-degree theoremScott SchubrEdition 3 · 2026-10-27 Public
  2. Finite positivity and correction inertia for the Riemann theta formScott SchubrEdition 2 · 2026-10-27 Public
  3. Minimum-Degree Obstructions in the Riemann Theta Product: Classification, transition bounds and robust Gram certificatesScott SchubrEdition 3 · 2026-10-27 Public
  4. Collision and cancellation spectra for concentrated energy formsScott SchubrEdition 2 · 2026-10-27 Public
  5. Fekete convergence from balanced integer predecessors in shrinking corridorsScott SchubrEdition 2 · 2026-10-27 Public
  6. Sharp trace-degree certificates for rank-two permanent-derivative compensationScott SchubrEdition 2 · 2026-10-27 Public
  7. Residual Certificates and Empirical Sharpness for Entropic Self-Transport ScoresScott SchubrEdition 2 · 2026-10-27 Public
  8. Observation norms under double-exponential confinementScott SchubrEdition 2 · 2026-10-27 Public
  9. Residual Stopping and Pointwise Inference for Nonuniform Entropic Self-TransportScott SchubrEdition 2 · 2026-10-27 Public
  10. Finite-spectral recovery of Weyl-blind twisting modesScott SchubrEdition 2 · 2026-10-27 Public
  11. Local comparison counting for linear extensions and a bounded-range balance refinementScott SchubrEdition 2 · 2026-10-27 Public
  12. An explicit hyperbolicity threshold for xi Jensen polynomialsScott SchubrEdition 2 · 2026-10-27 Public
  13. A quantitative Chollet inequality for rank-four matrices of order sevenScott SchubrEdition 2 · 2026-10-27 Public
  14. Single-copy learning of stabilizers with correlated diagonal noiseScott SchubrEdition 2 · 2026-10-27 Public
  15. Relative finite optimization of arithmetic approximation distancesScott SchubrEdition 2 · 2026-10-27 Public
  16. Growing null subtraction and weighted Weil zero detectionScott SchubrEdition 2 · 2026-10-27 Public
  17. Frequency Localization for Weil Operator CertificatesScott SchubrEdition 3 · 2026-10-27 Public
  18. Sharp logarithmic sampling thresholds and lacunary interpolation in the Báez–Duarte step spaceScott SchubrEdition 2 · 2026-10-27 Public
  19. Joint Cutoffs and Negative-Spectrum Decay for Weighted Weil OperatorsScott SchubrEdition 3 · 2026-10-27 Public
  20. Sharp convergence of heat-kernel Sinkhorn metricsScott SchubrEdition 2 · 2026-10-27 Public
  21. Positive heat-flow observations on spherical shells: cutoffs, optimal preparation and concentrationScott SchubrEdition 2 · 2026-10-27 Public
  22. Curvature classification and certified Sinkhorn metrics for Fourier density modelsScott SchubrEdition 2 · 2026-10-27 Public
  23. Mean ergodic convergence from near-diagonal subadditivityScott SchubrEdition 2 · 2026-10-27 Public
  24. Quantitative Null-Space Compression for a Weighted Weil OperatorScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 4

Single-time boundary heat-flux rigidity for smooth domains

Scott Schubr

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Abstract

We study recovery of a domain from the entire boundary heat flux at one positive time, for Dirichlet evolution with initial temperature one. Near a ball, after fixing volume and centroid, the flux defect in C^(m−1,α) controls the radial deformation in C^(m,α), where m≥3 and 0<α<1. Dividing the flux by its physical boundary mean gives one stability constant and one shape neighborhood valid for every observation time T≥ T₀>0. This normalization removes the exponential late-time loss of the absolute flux signal; it does not remove sensitivity to fixed absolute measurement noise. The proof combines strict positivity of the spherical heat multipliers above translations with uniform shape-differentiable convergence to the normalized first-eigenfunction flux. We also give a moving-plane proof that constant signed flux on every boundary component at one time forces a bounded connected smooth domain to be a ball, without convexity or connected boundary. In contrast, a moving proper observation cap admits infinitely many nearby normalized nonballs with exactly the ball flux at the prescribed time.

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