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 functional | Statement: [Eugenio Calabi, knownFor, Calabi functional]

Target entity: Calabi functional
Context triple: [Eugenio Calabi, knownFor, Calabi functional]

• A. Calabi–Yau metric
  A Calabi–Yau metric is a special Ricci-flat Kähler metric with SU(n) holonomy that endows Calabi–Yau manifolds with their characteristic geometric and physical properties.
• B. Calabi conjecture
  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.
• C. Kähler–Ricci flow
  Kähler–Ricci flow is a geometric evolution equation that deforms Kähler metrics on complex manifolds according to their Ricci curvature, playing a central role in complex differential geometry and the study of canonical metrics.
• D. Monge–Ampère equation
  The Monge–Ampère equation is a fully nonlinear partial differential equation central to differential geometry, optimal transport, and several complex variables, often used to study curvature and geometric structures.
• E. Perelman’s entropy functionals
  Perelman’s entropy functionals are analytic quantities introduced by Grigori Perelman to study the behavior and singularities of the Ricci flow, playing a central role in his proof of the Poincaré and geometrization conjectures.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Calabi functional
Target entity description: The Calabi functional is a key tool in complex differential geometry that measures the deviation of a Kähler metric from having constant scalar curvature, central to the study of extremal Kähler metrics and stability.

• A. Calabi–Yau metric
  A Calabi–Yau metric is a special Ricci-flat Kähler metric with SU(n) holonomy that endows Calabi–Yau manifolds with their characteristic geometric and physical properties.
• B. Calabi conjecture
  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.
• C. Kähler–Ricci flow
  Kähler–Ricci flow is a geometric evolution equation that deforms Kähler metrics on complex manifolds according to their Ricci curvature, playing a central role in complex differential geometry and the study of canonical metrics.
• D. Monge–Ampère equation
  The Monge–Ampère equation is a fully nonlinear partial differential equation central to differential geometry, optimal transport, and several complex variables, often used to study curvature and geometric structures.
• E. Perelman’s entropy functionals
  Perelman’s entropy functionals are analytic quantities introduced by Grigori Perelman to study the behavior and singularities of the Ricci flow, playing a central role in his proof of the Poincaré and geometrization conjectures.
• F. None of above. chosen