Construct a surgery process from measured comparison data
ProvedOpenGA.nonempty_surgeryComparisonProcess_of_measuredDatabishop-gromovgeometric-analysispoincare-conjecture
Measured radial volume-control data and scalar/width profiles determine a surgery comparison process with the same initial-width bound and final time. The only missing budget field, positivity of its reference anchor, is derived from the measured reference ball. The uniform radial lower bound, density comparison, removed-volume containment and budget are retained as hypotheses. This proves an adapter between analytic interfaces, not the existence of a Ricci flow.
Preamble
import Definitions.Def_OpenGA_MeasuredSurgeryComparisonData set_option autoImplicit false open MeasureTheory Set Filter open scoped Manifold ContDiff ENNReal BigOperators Topology open DifferentialGeometry.Geometry.Riemannian.VolumeComparison open OpenGA
Formal statement
theorem OpenGA.nonempty_surgeryComparisonProcess_of_measuredData {W T : ℝ} (D : MeasuredSurgeryComparisonData W T) : Nonempty (SurgeryComparisonProcess W T) := by sorrySource