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  1. Certified source elimination for localized odd Weil formsScott SchubrEdition 2 · 2026-10-27 Public
  2. Trace-perturbed minimizers of the mixed discriminantScott SchubrEdition 2 · 2026-10-27 Public
  3. Single-copy learning of noisy stabilizers by certified filteringScott SchubrEdition 2 · 2026-10-27 Public
  4. Exponential growth of sparse Euler products and normal graded domainsScott SchubrEdition 2 · 2026-10-27 Public
  5. Phase transitions and effective curvature bounds in Fourier density modelsScott SchubrEdition 2 · 2026-10-27 Public
  6. Sharp Stability and Geometric Classification of a Vámos Quartic DeformationScott SchubrEdition 2 · 2026-10-27 Public
  7. Strong permanent inequalities for cycles and a class of single-chord supportsScott SchubrEdition 2 · 2026-10-27 Public
  8. Sharp Quadratic Smoothing for Truncated Simplex SumsScott SchubrEdition 2 · 2026-10-27 Public
  9. Sharp limitations of two permanental cofactor comparisonsScott SchubrEdition 2 · 2026-10-27 Public
  10. Three-point positivity for weighted products of Riemann theta density powersScott SchubrEdition 2 · 2026-10-27 Public
  11. Strong permanent inequalities on three chorded seven-cycle supportsScott SchubrEdition 2 · 2026-10-27 Public
  12. Coupled permanent cofactors: sharp occupation bounds and compensation geometryScott SchubrEdition 11 · 2026-10-27 Public
  13. Strong permanent inequalities for three-row bipartite supports and triangle-free supports through order sevenScott SchubrEdition 2 · 2026-10-27 Public
  14. Strong permanent contraction on four-row bipartite supports through six columnsScott SchubrEdition 2 · 2026-10-27 Public
  15. Strong permanent contraction on four-by-seven bipartite supportsScott SchubrEdition 2 · 2026-10-27 Public
  16. Finite-order positivity and growing negative inertia for averaged Riemann theta productsScott SchubrEdition 2 · 2026-10-27 Public
  17. Row-dependent bounds for strong permanent contraction on four-by-eight supportsScott SchubrEdition 2 · 2026-10-27 Public
  18. Compact capture and protected bridges on the Koras–Russell cylinderScott SchubrEdition 2 · 2026-10-27 Public
  19. Dimension-dependent holomorphic certificate degrees on zero-sum hyperplanesScott SchubrEdition 2 · 2026-10-27 Public
  20. Admissible kernel lifts with positive endpoint forms and nonreal Fourier zerosScott SchubrEdition 2 · 2026-10-27 Public
  21. Global finite-depth stability and nonreal zeros of admissible Fourier transformsScott SchubrEdition 2 · 2026-10-27 Public
  22. A Weyl Law for Rapidly Twisted Polar-Strip TubesScott SchubrEdition 2 · 2026-10-27 Public
  23. Weighted polynomial localization and theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  24. Weyl Laws and Angular Stability for Rapidly Twisted TubesScott 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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