Realize a nonzero stable tube class by a generating family, prove injectivity using two momenta, and apply one-critical-point vanishing after hypothetical transport.
Proof overview available
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The two papers establish the equivalence between Gigli’s distributional curvature lower bound and an Alexandrov lower curvature bound, together with the weak-Hessian theorem used in the converse.
All 2 overviews available
The catalogue synthesis connects the results, proof strategies, and theorems used across these manuscripts.