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gptkbp:instance_of
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gptkb:Mathematics
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gptkbp:applies_to
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Riemannian manifolds
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gptkbp:can_lead_to
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formation of singularities
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gptkbp:challenges
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gptkb:students
computational complexity
singularity analysis
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gptkbp:collaborated_with
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research groups
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gptkbp:developed_by
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gptkb:Richard_S._Hamilton
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https://www.w3.org/2000/01/rdf-schema#label
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Ricci flow with surgery
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gptkbp:integrates_with
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modern mathematical research
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gptkbp:involves
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surgery techniques
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gptkbp:is_a
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method for evolving metrics
method in geometric analysis
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gptkbp:is_analyzed_in
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research articles
topological methods
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gptkbp:is_applied_in
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gptkb:string_theory
mathematical modeling
non-compact manifolds
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gptkbp:is_associated_with
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Ricci curvature
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gptkbp:is_challenged_by
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alternative theories
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gptkbp:is_characterized_by
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deformation of the metric
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gptkbp:is_collaborative_with
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other mathematical fields
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gptkbp:is_connected_to
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differential equations
Einstein metrics
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gptkbp:is_considered
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mathematical physics
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gptkbp:is_critiqued_by
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mathematical reviews
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gptkbp:is_discussed_in
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gptkb:academic_conferences
online forums
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gptkbp:is_documented_in
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gptkb:textbooks
mathematical literature
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gptkbp:is_enhanced_by
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new techniques
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gptkbp:is_essential_for
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3-manifold topology
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gptkbp:is_evaluated_by
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peer review
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gptkbp:is_examined_in
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gptkb:Mathematician
graduate studies
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gptkbp:is_explored_in
|
case studies
numerical analysis
theoretical mathematics
mathematical seminars
doctoral theses
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gptkbp:is_fundamental_to
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understanding geometric structures
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gptkbp:is_implemented_in
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numerical simulations
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gptkbp:is_influenced_by
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historical developments in geometry
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gptkbp:is_influential_in
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modern geometry
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gptkbp:is_interdisciplinary_with
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physics and engineering
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gptkbp:is_noted_for
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its complexity
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gptkbp:is_part_of
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geometric topology
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gptkbp:is_promoted_by
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gptkb:educational_institutions
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gptkbp:is_recognized_by
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mathematical societies
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gptkbp:is_reflected_in
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research papers
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gptkbp:is_related_to
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gptkb:Perelman’s_proof_of_the_Poincaré_conjecture
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gptkbp:is_studied_for
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its applications in topology
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gptkbp:is_studied_in
|
differential geometry
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gptkbp:is_supported_by
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grants
computational tools
academic funding
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gptkbp:is_taught_in
|
advanced mathematics courses
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gptkbp:is_used_to
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prove geometrization conjecture
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gptkbp:is_utilized_by
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theoretical physicists
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gptkbp:is_utilized_for
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understanding curvature behavior
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gptkbp:is_utilized_in
|
research collaborations
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gptkbp:key
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solving geometric problems
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gptkbp:presented_by
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symposiums
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gptkbp:provides
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singularity formation analysis
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gptkbp:published_by
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mathematical journals
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gptkbp:related_to
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gptkb:Ricci_flow
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gptkbp:requires
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initial conditions
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gptkbp:used_in
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geometric analysis
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gptkbp:bfsParent
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gptkb:Poincaré_conjecture
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gptkbp:bfsLayer
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