OAI/Geometry/SurfaceImmersion/Atlas/PhaseMetricConvexity.lean

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3 declarations, 0 contain sorry, 0 declared as axioms

Strict convexity of the prescribed surface metric gives the exact positive transverse Hessian used by the actual phase-coordinate loop.

  1. lemma OAI.ClosedSurfaceR4.coordinateMetricHessian_congr_germ line 18
  2. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SmoothingAtlas.realChartMap_metric_germ line 39
  3. theorem OAI.ClosedSurfaceR4.FiniteOrderSmoothing.SmoothingAtlas.phase_hessian_positive_of_metric line 68