Top Open Problems
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-5451 Compact-dual cone decomposition and an escaping-curve certificate
- Math-5452 Boundary-sensitive extensions of the Thurston metric
- Math-5453 A first-kind regular cover with variable critical exponent
- Math-5454 Critical exponents converge under the metric-ball subgroup exhaustion
- Math-5455 The Thurston metric on the punctured-torus plane
- Math-5456 Minimal-area conformal metrics and a thick-part Thurston bound
- Math-5457 The Thurston metric for unit-volume flat n-tori
- Math-5458 Normalized least-Lipschitz geometry beyond the hyperbolic locus
- Math-5459 Normalized obstructions to pointwise quarter-pinched collapse
- Math-5460 Flow-Morse functions and suspension examples
- Math-5461 Lipschitz homotopy groups and a quantitative size filtration
- Math-5462 Weighted infinite tori as quantitative phase spaces
- Math-5463 A flat counterexample and an exact symmetry-degree formula
- Math-5464 Integral symplectic pencils give compact fat torus bundles
- Math-5465 Reduction, holonomy, and symplectic-pencil obstructions
- Math-5466 Exact metric lifting, orbifold sufficiency, and a singular even-jet obstruction
- Math-5467 Completeness is essential for the fixed-circle length question
- Math-5468 An explicit infinite nonsymmetric cohomogeneity-one family
- Math-5469 The literal polar-rigidity question is false, with a sharp repaired theorem
- Math-5470 Rank-one no-new theorem for quasi-positive Geroch quotients
- Math-5471 Fundamental groups under quasi- and almost-positive curvature
- Math-5472 Quotient Ricci flow as a coupled and weighted super-Ricci flow
- Math-5473 Generic specialization and wall cancellation for Witt–Toledo classes
- Math-5474 The K2 avatar of the higher Weil-Petersson form
- Math-5475 Complex-structure dependence of cyclotomic Hitchin loci
- Math-5476 Baker's Dozen — Lorentzian Birkhoff theorem
- Math-5477 Baker's Dozen — Periodic multidimensional outer-billiard trajectories
- Math-5478 Baker's Dozen — A converse Desargues theorem
- Math-5479 Baker's Dozen — Relations among triangle areas
- Math-5480 Questions in Geometric Group Theory — Q 1.12
- Math-5481 Questions in Geometric Group Theory — Q 2.18
- Math-5482 Questions in Geometric Group Theory — Q 3.9
- Math-5483 Questions in Geometric Group Theory — Q 3.11
- Math-5484 Questions in Geometric Group Theory — Q 5.1
- Math-5485 Questions in Geometric Group Theory — Q 12.1
- Math-5486 Some Questions — Question 4
- Math-5487 Some Questions — Question 15
- Math-5488 Some Questions — Question 22
- Math-5489 Some Questions — Question 25
- Math-5490 Some Questions — Question 36
- Math-5491 Some Questions — Question 43
- Math-5492 Geometry of Continued Fractions — Integer trigonometry and IKEA problem
- Math-5493 Some Open Problems in Elasticity — Smooth self-contact
- Math-5494 Open Problems in Integrable Systems — Topology of integrable systems, Lagrangian fibrations, and their invariants
- Math-5495 Open Problems in Integrable Systems — Polynomial in momenta integrals in higher dimensions.
- Math-5496 Open Problems in Integrable Systems — Polynomial in momenta integrals in higher dimensions.
- Math-5497 Open Problems in Integrable Systems — Around the Birkhoff conjecture
- Math-5498 Open Problems in Integrable Systems — Geometry of caustics, invariant surfaces, and commuting billiard maps
- Math-5499 Open Problems in Integrable Systems — Geometry of caustics, invariant surfaces, and commuting billiard maps
- Math-5500 Open Problems in Integrable Systems — Argument shift method and Jordan-Kronecker invariants of Lie algebras