Geometry
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-2240 Finding matching upper and lower bounds for k-sets and halving lines
- Math-2296 Universal optimality beyond rapidly decaying completely monotone potentials
- Math-2297 ALE singularities: Type-II existence and a bounded-scalar scale-energy certificate
- Math-2298 Finite traceless-Ricci budget and Ricci-flat bubbles under bounded scalar curvature
- Math-2299 Endpoint Ricci-energy balance and Weyl-dominated blow-ups under bounded scalar curvature
- Math-2300 A hyperbolic geodesic and the robust infinite branch
- Math-2301 Closed geodesics in a finite-volume torus ansatz
- Math-2302 No conjugate points: flat-growth rigidity and the three-dimensional residue
- Math-2316 Linear-Programming Sharpness and Universal Lattice Optimality
- Math-2339 Convexity of Injectivity Loci Under MTW
- Math-2356 Birkhoff Conjecture for Integrable Convex Billiards
- Math-2364 Rational Ellipticity, Entropy, Euler Characteristic, and Formality
- Math-2393 Homogeneity of Fano Contact Manifolds
- Math-2400 Spectrahedrality of Hyperbolicity Cones
- Math-2401 Vanishing of the $hat A$-Genus Under Nonnegative Curvature
- Math-2402 Gromov Macroscopic Dimension Conjecture
- Math-2416 Petty's projection-body conjecture
- Math-2441 Minimum Distinct Distances Among Planar Point Sets
- Math-2442 Falconer Distance Conjecture in the Plane
- Math-2449 Mahler’s Volume Conjecture
- Math-2450 Planar Log-Brunn–Minkowski After Translation
- Math-2451 The $L_p$ Brunn–Minkowski Conjecture
- Math-2464 The Tamed-to-Compatible Symplectic Conjecture
- Math-2490 Borsuk Partition Problem in Dimensions Four Through Sixty-Three
- Math-2504 Optimal Covering Density of Euclidean Balls
- Math-2628 Triangular-cylinder approximation of aligned radial sweeps
- Math-2629 Half-minimum-area bound for cylinder covers
- Math-2630 Linear coefficient of minimum spherical logarithmic energy
- Math-2631 Binary edit distance has exponential-scale L1 distortion
- Math-2632 Uniform L1 distortion for bounded treewidth
- Math-2633 Simplex maximum for projection-body volume
- Math-2634 Directionwise normalized cylinder-covering bound
- Math-2635 Sharp exponential scale of edit-distance distortion
- Math-2636 One signing for all Euclidean prefixes
- Math-2637 Euclidean Steinitz–Bergström bound
- Math-2638 Gaussian propeller partition bound
- Math-2639 Logarithmic Sobolev inequality from subgaussian marginals
- Math-2640 Sharp entropy lower bound for log-concave densities
- Math-2641 Subpolynomial nonlinear dimension reduction in Lp
- Math-2642 Liftability without spectrahedrality for a hyperbolicity cone
- Math-2643 Uniform L1 distortion of planar graph metrics
- Math-2644 Projected Lax conjecture
- Math-2645 Finite cylinder approximation of ruled sets
- Math-2646 Single-lattice covering density of order n log n
- Math-2647 Gromov width of symmetric polar products
- Math-2648 Worst-case symmetric translative covering density
- Math-2649 Triangular minimum of planar Coulomb renormalized energy
- Math-2650 Affine Bernstein assertion for entire graphs in dimension ten
- Math-2651 Affine Bernstein assertion in dimensions three through nine
- Math-2652 Analytic path selection at several exponential ends