4 papers
Blaschke Conjecture and Complex Geometry
Kyobeom Song
We provide a complex-geometric approach to the Blaschke conjecture, i.e., that a manifold whose injectivity radius equals its diameter is isometric to a compact rank-one symmetric…
Revised Demailly's Affineness Criterion and Algebraization of Entire Grauert Tubes
Kyobeom Song
We provide a partial answer to Burns' 1982 conjecture on the affineness of entire Grauert tubes: the complement of a codimension-one subset of an entire Grauert tube is affine. Thi…
A Note on Zoll Manifolds with Entire Grauert Tubes
Kyobeom Song
We compute several algebraic indices of the algebraization of the tangent bundle of a Zoll manifold that admits an entire Grauert tube. As an application, we prove that any Zoll ma…
Zoll Manifolds of Type with Entire Grauert Tubes
Chi Li, Kyobeom Song
We show that a Zoll manifold of type with an entire Grauert tube is isometric to with the canonical Fubini-Study metric, up to constant multiplicati…