Curved-space isoperimetric and filling reference

Family 337: Sharp Cartan–Hadamard isoperimetry and rigidity. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Geometry and transport researchers can compare area/volume bounds in complete simply connected nonpositive-curvature or proper CAT0 settings.

Applicability and commercial boundary

A sharp inequality does not provide a minimizer algorithm for an arbitrary discrete mesh; global curvature and finite-perimeter hypotheses matter.

Initial business decision

Research or conditional engineering only. A practical implementation, recurring buyer problem and willingness to pay have not been established. Mathematical usefulness alone is insufficient evidence for a standalone lucrative product.

Next verification action

Extract an exact model-ball reference and a separately justified mesh approximation.

Evidence scope

The catalog statement was individually reviewed. The manuscript proof and formal-scope comparison remain queued. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.

Generalized Cartan–Hadamard isoperimetry and Euclidean equality rigidity.