Sections / Section 5: General Hessian and Isoquant Geometry / intrinsic_always_nonneg

Intrinsic Always Nonneg

theoremprovedFoundations

Documentation

Lean 4 Proof

theorem intrinsic_always_nonneg (ρ c : ℝ) :
    0 ≤ sectionalCurvature J ρ c :=
  sectionalCurvature_nonneg ρ c

Dependency Graph

Location

thesis/CESProofs/Foundations/IsoquantGeometry.lean:223

Module Section

Differential Geometry of CES Isoquants (Gap #6)

In the same file

gradientNormSq unitNormalComponent gradientNormSq_pos tangentSpace_is_onePerp induced_metric_eq_vecNormSq secondFundamentalFormQF gaussCurvature meanCurvatureTrace curvature_eq_neg_eigenvalue_sqrt secondFF_from_hessian gaussCurvature_pos meanCurvature_pos sectionalCurvature sectionalCurvature_nonneg sectionalCurvature_eq_zero_iff sectionalCurvature_explicit sectionalCurvature_from_K principalCurvature_trichotomy isoquant_umbilic spaceForm_at_symmetry