Fields / Differential geometry
Catalogues in this field Official catalogue numbers 338 Follow the analytic estimates, shrinking coordinates, and surjectivity argument toward biholomorphic uniformization under positive bisectional curvature.
Proof overview available The catalogue guide leads to the article, its external inputs, and the bilingual PDF editions.
Open the catalogue guide→ Proof overviews (1) Official catalogue order 01 Uniformization of complete Kähler manifolds with positive bisectional curvature → 356 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.
Explore the synthesis and connections→ Proof overviews (2) Official catalogue order 01 Gigli’s distributional curvature characterization of Alexandrov spaces → 02 Weak Hessian bounds along every geodesic in RCD spaces → 357 Follow the compensation for scale-dependent degeneration of harmonic coordinates in value space, leading to all-pairs metric bounds and an open image.
Proof overview available The catalogue guide leads to the article, its external inputs, and the bilingual PDF editions.
Open the catalogue guide→ Proof overviews (1) Official catalogue order 01 Bi-Lipschitz Coordinates at Regular Points of Noncollapsed RCD Spaces →