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: Monge–Ampère equations | Statement: [Shing-Tung Yau, knownFor, Monge–Ampère equations]

Target entity: Monge–Ampère equations
Context triple: [Shing-Tung Yau, knownFor, Monge–Ampère equations]

• A. Monge–Ampère equation chosen
  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.
• B. Nirenberg problem in differential geometry
  The Nirenberg problem in differential geometry is a classical question about prescribing Gaussian curvature on the 2-sphere via conformal deformations of the metric.
• C. Christoffel–Minkowski problem
  The Christoffel–Minkowski problem is a classical question in convex geometry that seeks to reconstruct a convex body from prescribed curvature or area measure data on the unit sphere.
• D. 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.
• E. Monge problem in optimal transport
  The Monge problem in optimal transport is a foundational mathematical formulation that seeks the most efficient way to move mass from one distribution to another, minimizing a given transportation cost.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.