Calabi–Bernstein theorem

Target entity: Calabi–Bernstein theorem
Context triple: [Eugenio Calabi, knownFor, Calabi–Bernstein theorem]

• A. 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.
• 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. Kodaira vanishing theorem
  The Kodaira vanishing theorem is a fundamental result in algebraic geometry that gives conditions under which certain cohomology groups of ample line bundles on smooth projective varieties vanish, with deep implications for the classification of complex manifolds.
• 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. 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.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Calabi–Bernstein theorem
Target entity description: The Calabi–Bernstein theorem is a result in differential geometry that characterizes entire maximal spacelike hypersurfaces in Minkowski space as necessarily being affine hyperplanes.

• A. 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.
• 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. Kodaira vanishing theorem
  The Kodaira vanishing theorem is a fundamental result in algebraic geometry that gives conditions under which certain cohomology groups of ample line bundles on smooth projective varieties vanish, with deep implications for the classification of complex manifolds.
• 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. 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.
• F. None of above. chosen