Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Calabi conjecture | Statement: [Monge–Ampère equation, usedIn, Calabi conjecture]

Target entity: Calabi conjecture
Context triple: [Monge–Ampère equation, usedIn, Calabi conjecture]

• A. Calabi conjecture chosen
  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.
• B. 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.
• C. 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.
• D. 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.
• E. 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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.