Geometry problems

This area contains 111 revision-pinned source placements and 0 reviewed canonical dossiers. Placements may include aliases or duplicate claims.

Reviewed dossiers

No canonical dossier currently meets the publishability threshold.

Source placement records

• Abundance conjecture
• Bass conjecture on the finite generation of certain algebraic K-groups.
• Bass–Quillen conjecture
• Deligne conjecture
• Deligne's conjecture on Hochschild cohomology about the operadic structure on Hochschild cochain complex.
• Fröberg conjecture on the Hilbert functions of a set of forms.
• Fujita conjecture
• General elephant problem
• spherical
• Jacobian conjecture for two-dimensional spaces
• Maulik–Nekrasov–Okounkov–Pandharipande conjecture on an equivalence between Gromov–Witten theory and Donaldson–Thomas theory
• Nagata's conjecture on curves
• Nagata–Biran conjecture
• Nakai conjecture
• Parshin's conjecture
• Section conjecture
• Standard conjectures on algebraic cycles
• Tate conjecture
• Virasoro conjecture
• Zariski multiplicity conjecture on the topological equisingularity and equimultiplicity of varieties at singular points
• flips
• Resolution of singularities in characteristic p {\displaystyle p} {\displaystyle p}
• Borsuk's problem on upper and lower bounds for the number of smaller-diameter subsets needed to cover a bounded n-dimensional set.
• The covering problem of Rado
• The Erdős–Oler conjecture
• disk covering problem
• The kissing number problem for dimensions other than 1, 2, 3, 4, 8 and 24
• Reinhardt's conjecture
• Sphere packing
• Square packing in a square
• Ulam's packing conjecture about the identity of the worst-packing convex solid
• The Tammes problem for numbers of nodes greater than 14 (except 24).
• The spherical Bernstein's problem, a generalization of Bernstein's problem
• Carathéodory conjecture
• Cartan–Hadamard conjecture
• Chern's conjecture (affine geometry) that the Euler characteristic of a compact affine manifold vanishes.
• Chern's conjecture for hypersurfaces in spheres, a number of closely related conjectures.
• Closed curve problem
• filling area conjecture
• The Hopf conjectures relating the curvature and Euler characteristic of higher-dimensional Riemannian manifolds
• Osserman conjecture
• Yau's conjecture on the first eigenvalue
• big-line-big-clique conjecture
• The Dirac–Motzkin conjecture on the minimum number of ordinary lines for n points in the Euclidean plane
• The Hadwiger conjecture on covering n-dimensional convex bodies with at most 2 smaller copies
• Solving the happy ending problem for arbitrary n {\displaystyle n} {\displaystyle n}
• Improving lower and upper bounds for the Heilbronn triangle problem.
• Kalai's 3 conjecture on the least possible number of faces of centrally symmetric polytopes.
• The Kobon triangle problem on triangles in line arrangements
• The Kusner conjecture
• The McMullen problem on projectively transforming sets of points into convex position
• Opaque forest problem on finding opaque sets for various planar shapes
• Orchard-planting problem on the maximum number of 3-point lines attainable by a configuration of n points in the plane
• How many unit distances
• Finding matching upper and lower bounds for k-sets and halving lines
• crossing number
• Tripod packing
• Atiyah conjecture on configurations
• Bellman's lost-in-a-forest problem
• Borromean rings
• Connelly’s blooming conjecture
• Danzer's problem and Conway's dead fly problem
• Dissection into orthoschemes
• Ehrhart's volume conjecture
• Falconer's conjecture
• The values of the Hermite constants for dimensions other than 1–8 and 24
• holyhedron
• Inscribed square problem, also known as Toeplitz' conjecture and the square peg problem
• The Kakeya conjecture
• Weaire–Phelan structure
• Lebesgue's universal covering problem on the minimum-area convex shape in the plane that can cover any shape of diameter one
• Mahler's conjecture on the product of the volumes of a centrally symmetric convex body and its polar.
• Are the two Meissner tetrahedra the minimum-volume three-dimensional shapes of constant width?
• Moser's worm problem
• The moving sofa problem
• Can every spherical non-convex polyhedron that tiles space by translation have its faces grouped into patches with the same combin
• Voronoi diagram
• Is there a general expression for the minimum ropelength of an arbitrary closed knot?
• What constant 1
• Is the upper bound of a closed knot's minimum ropelength linear to its crossing number?
• Is there a general expression for how much the ends of a long rope of radius 1 get closer when a tight open knot is tied into it?
• Rupert's property
• Shephard's problem (a.k.a. Dürer's conjecture)
• more than seven faces
• The Thomson problem
• Convex uniform 5-polytopes
• Hilbert's third problem for non-Euclidean geometries
• Einstein problem (David Smith, Joseph Samuel Myers, Craig S. Kaplan, Chaim Goodman-Strauss, 2024)
• Maximal rank conjecture (Eric Larson, 2018)
• Weibel's conjecture (Moritz Kerz, Florian Strunk, and Georg Tamme, 2018)
• Willmore conjecture (Fernando Codá Marques and André Neves, 2012)
• Erdős distinct distances problem (Larry Guth, Nets Hawk Katz, 2011)
• Heterogeneous tiling conjecture (squaring the plane) (Frederick V. Henle and James M. Henle, 2008)
• Ending lamination theorem (Jeffrey F. Brock, Richard D. Canary, Yair N. Minsky, 2004)
• Carpenter's rule problem (Robert Connelly, Erik Demaine, Günter Rote, 2003)
• Lambda g conjecture (Carel Faber and Rahul Pandharipande, 2003)
• Nagata's conjecture (Ivan Shestakov, Ualbai Umirbaev, 2003)
• Double bubble conjecture (Michael Hutchings, Frank Morgan, Manuel Ritoré, Antonio Ros, 2002)
• Honeycomb theorem (Thomas Callister Hales, 1999)
• Lange's conjecture (Montserrat Teixidor i Bigas and Barbara Russo, 1999)
• Bogomolov conjecture (Emmanuel Ullmo, 1998, Shou-Wu Zhang, 1998)
• Kepler conjecture (Samuel Ferguson, Thomas Callister Hales, 1998)
• Dodecahedral conjecture (Thomas Callister Hales, Sean McLaughlin, 1998)