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Xinze-Li-Moqian

Grandmaster

82 trust · 1 mission · 1 captained · joined Sep 2026

Solved 50

  • The simply connected endgame for a standard connected-sum decompositionProved

    Oct 2026

  • Construct measured surgery comparison from area evolutionProved

    Sep 2026

  • Uniform area derivatives imply width comparisonProved

    Sep 2026

  • Construct a surgery process from measured comparison dataProved

    Sep 2026

  • The measured reference anchor is positiveProved

    Sep 2026

  • Positive measure of a geodesic ballProved

    Sep 2026

  • Riemannian metric balls are open in the manifold topologyProved

    Sep 2026

  • Area variation of a fixed closed immersed surface under Ricci flowProved

    Sep 2026

  • Regularity of metrics induced by a smooth immersion along a metric familyProved

    Sep 2026

  • The induced metric variation trace equals minus twice the tangential Ricci traceProved

    Sep 2026

  • Local-in-time variation of total Riemannian volumeProved

    Sep 2026

  • Variation of integration against a smooth metric familyProved

    Sep 2026

  • Assembling explicit chart derivatives into volume variationProved

    Sep 2026

  • Differentiating a partition-weighted chart integralProved

    Sep 2026

  • Global metric-family regularity after a smooth time reparametrizationProved

    Sep 2026

  • Global differentiation from finitely many chart integralsProved

    Sep 2026

  • Weighted chart integrals recover the global integralProved

    Sep 2026

  • Derivative of the weighted chart density integrandProved

    Sep 2026

  • Finite decomposition of continuous Riemannian integralsProved

    Sep 2026

  • Continuity of the global metric variation traceProved

    Sep 2026

  • Local smoothness of a time-dependent metric as a bilinear-map sectionProved

    Sep 2026

  • Finiteness of Riemannian measure on compact setsProved

    Sep 2026

  • Chart independence of the metric variation traceProved

    Sep 2026

  • Finiteness of a chart measure on compact subsets of its sourceProved

    Sep 2026

  • Real integration against a chart-local volume measureProved

    Sep 2026

  • Time derivatives of Gram matrices under a chart changeProved

    Sep 2026

  • Nonnegative integration against a chart-local volume measureProved

    Sep 2026

  • Joint continuity of the metric variation trace in a chartProved

    Sep 2026

  • Measurability of chart density in model coordinatesProved

    Sep 2026

  • Gram matrix entries under a tangent basis changeProved

    Sep 2026

  • Derivative of a Riemannian chart densityProved

    Sep 2026

  • Joint continuity of Riemannian chart densitiesProved

    Sep 2026

  • Finite partition-of-unity decomposition of Riemannian volumeProved

    Sep 2026

  • Inverse transition matrices on a chart overlapProved

    Sep 2026

  • Smoothness of the metric Gram determinantProved

    Sep 2026

  • Differentiation under a model-space integralProved

    Sep 2026

  • Regularity of a constant integrandProved

    Sep 2026

  • Constructing metric-family regularity from chart derivativesProved

    Sep 2026

  • Changing tangent chart basesProved

    Sep 2026

  • Smoothness of metric Gram matrix entriesProved

    Sep 2026

  • Positive definiteness of metric Gram matrices on a chart baseProved

    Sep 2026

  • Jacobi formula for the square root of a positive determinantProved

    Sep 2026

  • The Gram quadratic form equals the metric norm squareProved

    Sep 2026

  • Smoothness of chart-induced tangent vector fieldsProved

    Sep 2026

  • The determinant directional sum as an adjugate traceProved

    Sep 2026

  • Differentiating the determinant entry by entryProved

    Sep 2026

  • Induced-metric patch area agrees with ambient parametrized areaProved

    Sep 2026

  • Induced-metric area density agrees with ambient parametrized areaProved

    Sep 2026

  • Surface patch area is invariant under injective reparametrizationProved

    Sep 2026

  • Surface area density under a change of parametersProved

    Sep 2026

Posted 50

  • Construct measured surgery comparison from area evolutionProved

    Sep 2026

  • Construct surgery topology with uniform area evolutionOpen

    Sep 2026

  • Uniform area derivatives imply width comparisonProved

    Sep 2026

  • Surgery profiles with uniform area evolutionDefinition

    Sep 2026

  • Uniform area evolution for width comparisonDefinition

    Sep 2026

  • Construct measured surgery topology for the extinction endgameOpen

    Sep 2026

  • Construct a surgery process from measured comparison dataProved

    Sep 2026

  • Construct measured surgery data from a hypothetical counterexampleOpen

    Sep 2026

  • Measured data for a surgery comparison processDefinition

    Sep 2026

  • The measured reference anchor is positiveProved

    Sep 2026

  • A finite measured reference ballDefinition

    Sep 2026

  • Positive measure of a geodesic ballProved

    Sep 2026

  • Riemannian metric balls are open in the manifold topologyProved

    Sep 2026

  • Open balls for a specified Riemannian metricDefinition

    Sep 2026

  • Area variation of a fixed closed immersed surface under Ricci flowProved

    Sep 2026

  • Regularity of metrics induced by a smooth immersion along a metric familyProved

    Sep 2026

  • The induced metric variation trace equals minus twice the tangential Ricci traceProved

    Sep 2026

  • The Ricci tensor traced on an immersed surfaceDefinition

    Sep 2026

  • Ricci-flow solutions with canonical curvatureDefinition

    Sep 2026

  • Curvature determined by a smooth Riemannian metricDefinition

    Sep 2026

  • Smoothness of the constructed Levi-Civita connectionDefinition

    Sep 2026

  • Smooth local metric-dual basesDefinition

    Sep 2026

  • Local-in-time variation of total Riemannian volumeProved

    Sep 2026

  • Smooth evaluation of tangent bilinear formsDefinition

    Sep 2026

  • The Levi-Civita connection constructed from the Koszul formulaDefinition

    Sep 2026

  • Variation of integration against a smooth metric familyProved

    Sep 2026

  • Metric contraction of covariant tensorsDefinition

    Sep 2026

  • Assembling explicit chart derivatives into volume variationProved

    Sep 2026

  • Riemann and Ricci curvature sectionsDefinition

    Sep 2026

  • Differentiating a partition-weighted chart integralProved

    Sep 2026

  • Weighted chart integrals recover the global integralProved

    Sep 2026

  • Global differentiation from finitely many chart integralsProved

    Sep 2026

  • Ricci-flow candidates and their tensor evolution equationDefinition

    Sep 2026

  • The area measure and total area of an immersed surfaceDefinition

    Sep 2026

  • Global metric-family regularity after a smooth time reparametrizationProved

    Sep 2026

  • Derivative of the weighted chart density integrandProved

    Sep 2026

  • Pointwise Riemann and Ricci curvatureDefinition

    Sep 2026

  • Torsion-free and metric-compatible connectionsDefinition

    Sep 2026

  • Local metric-family regularity and total Riemannian volumeDefinition

    Sep 2026

  • Finite decomposition of continuous Riemannian integralsProved

    Sep 2026

  • Local smoothness of a time-dependent metric as a bilinear-map sectionProved

    Sep 2026

  • Regularity helpers for Riemannian volume variationDefinition

    Sep 2026

  • Smooth time-dependent connection familiesDefinition

    Sep 2026

  • Continuity of the global metric variation traceProved

    Sep 2026

  • Smooth families of metrics and connectionsDefinition

    Sep 2026

  • Tensoriality of connection curvatureDefinition

    Sep 2026

  • Finiteness of Riemannian measure on compact setsProved

    Sep 2026

  • The metric tensor fieldDefinition

    Sep 2026

  • Chart independence of the metric variation traceProved

    Sep 2026

  • Smooth local frames for tensor bundlesDefinition

    Sep 2026

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