Calabi conjecture

Target entity: Calabi conjecture
Context triple: [Kähler–Ricci flow, relatedTo, Calabi conjecture]

• A. Donaldson–Uhlenbeck–Yau theorem
  The Donaldson–Uhlenbeck–Yau theorem is a fundamental result in differential and algebraic geometry that characterizes when a holomorphic vector bundle over a compact Kähler manifold admits a Hermitian–Einstein metric, linking geometric stability with the existence of such metrics.
• B. Poincaré conjecture
  The Poincaré conjecture is a landmark problem in topology that characterizes the three-dimensional sphere among three-dimensional manifolds and was famously solved by Grigori Perelman in the early 2000s.
• C. Yamabe problem
  The Yamabe problem is a fundamental question in differential geometry concerning whether every compact Riemannian manifold admits a metric of constant scalar curvature within a given conformal class.
• D. Hodge Conjecture
  The Hodge Conjecture is a major unsolved problem in algebraic geometry that predicts which cohomology classes on a non-singular projective complex variety arise from algebraic subvarieties.
• E. Strominger–Yau–Zaslow conjecture
  The Strominger–Yau–Zaslow conjecture is a proposal in mirror symmetry stating that mirror pairs of Calabi–Yau manifolds can be understood as dual special Lagrangian torus fibrations, providing a geometric explanation of mirror symmetry.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Calabi conjecture
Target entity description: The Calabi conjecture is a fundamental result in complex differential geometry, proved by Shing-Tung Yau, which characterizes when a compact Kähler manifold admits a unique Ricci-flat Kähler metric in a given Kähler class.

• A. Donaldson–Uhlenbeck–Yau theorem
  The Donaldson–Uhlenbeck–Yau theorem is a fundamental result in differential and algebraic geometry that characterizes when a holomorphic vector bundle over a compact Kähler manifold admits a Hermitian–Einstein metric, linking geometric stability with the existence of such metrics.
• B. Poincaré conjecture
  The Poincaré conjecture is a landmark problem in topology that characterizes the three-dimensional sphere among three-dimensional manifolds and was famously solved by Grigori Perelman in the early 2000s.
• C. Yamabe problem
  The Yamabe problem is a fundamental question in differential geometry concerning whether every compact Riemannian manifold admits a metric of constant scalar curvature within a given conformal class.
• D. Hodge Conjecture
  The Hodge Conjecture is a major unsolved problem in algebraic geometry that predicts which cohomology classes on a non-singular projective complex variety arise from algebraic subvarieties.
• E. Strominger–Yau–Zaslow conjecture
  The Strominger–Yau–Zaslow conjecture is a proposal in mirror symmetry stating that mirror pairs of Calabi–Yau manifolds can be understood as dual special Lagrangian torus fibrations, providing a geometric explanation of mirror symmetry.
• F. None of above. chosen