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: theory of Riemann surfaces | Statement: [Runge approximation theorem, usedIn, theory of Riemann surfaces]

Target entity: theory of Riemann surfaces
Context triple: [Runge approximation theorem, usedIn, theory of Riemann surfaces]

• A. Riemann surfaces chosen
  Riemann surfaces are one-dimensional complex manifolds that provide the natural geometric setting for studying complex analytic functions and their multi-valued behavior.
• B. Teichmüller theory
  Teichmüller theory is a branch of complex analysis and geometry that studies the deformation spaces of Riemann surfaces and their moduli, often via quasiconformal mappings.
• C. Riemann–Roch theorem
  The Riemann–Roch theorem is a fundamental result in algebraic geometry and complex analysis that relates the dimension of spaces of meromorphic sections of a line bundle on a curve to topological data such as genus and degree.
• D. Teichmüller space
  Teichmüller space is a parameter space in complex analysis and geometry that classifies all marked conformal or hyperbolic structures on a given topological surface up to equivalence.
• E. Nevanlinna theory
  Nevanlinna theory is a branch of complex analysis that studies the value distribution of meromorphic functions, quantifying how often they take or omit certain values.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.