clopen.solutions

Open problems

1131 registered problems.

OP-01101 Open
Dynamic planar nearest neighbors in logarithmic time
MG · data structures · dynamic convex hull · dynamic nearest neighbor · The Open Problems Project
OP-01102 Open
Edge-unfolding polycubes
MG · edge unfolding · orthogonal polyhedra · polycubes · The Open Problems Project
OP-01103 Open
Reflexivity of planar point sets
MG · polygonization · reflexivity · reflex vertices · The Open Problems Project
OP-01104 Open
Rolling a die over a fully labelled board
CO · computational complexity · grid puzzle · rolling cube puzzle · The Open Problems Project
OP-01105 Open
Immersed spheres made of regular pentagons
MG · dodecahedra · polyhedral surface · regular pentagons · The Open Problems Project
OP-01106 Open
Slicing axis-parallel rectangles with few lines
CO · axis-parallel rectangles · independent set · piercing number · The Open Problems Project
OP-01107 Open
Edge-coloring complete geometric graphs without monochromatic crossings
CO · complete geometric graph · crossing edges · edge coloring · The Open Problems Project
OP-01108 Open
Zipper unfoldings of convex polyhedra
MG · convex polyhedra · Hamiltonian path · The Open Problems Project · zipper unfolding
OP-01109 Open
A parallel null direction in higher-order symmetric spacetimes
DG · AIM Open Applied Problems · higher-order symmetric spaces · Lorentzian manifolds · parallel null vector fields
OP-01110 Open
A uniform Monte Carlo rate for the extended ensemble Kalman–Bucy filter
PR · AIM Open Applied Problems · ensemble Kalman filters · extended Kalman filters · propagation of chaos
OP-01111 Open
Bartnik's cosmological splitting conjecture
DG · AIM Open Applied Problems · cosmological spacetimes · Lorentzian splitting theorems · timelike geodesic completeness
OP-01112 Open
Completeness under conformal changes of compact Lorentzian spaceforms
DG · AIM Open Applied Problems · conformal changes · geodesic completeness · Lorentzian spaceforms
OP-01113 Open
Does a multivariate Riccati diffusion forget its initial covariance under common noise?
PR · AIM Open Applied Problems · contraction estimates · ensemble Kalman filters · Riccati diffusions
OP-01114 Open
Does Cameron–Martin coercivity ensure a strong posterior mode?
PR · AIM Open Applied Problems · Gaussian measures · maximum a posteriori estimators · small-ball modes
OP-01115 Open
Does the silver exponent remain optimal when gradient steps may be negative?
OC · AIM Open Applied Problems · first-order methods · gradient descent · stepsize schedules
OP-01116 Open
Future timelike completeness and a CMC Cauchy hypersurface
DG · AIM Open Applied Problems · constant mean curvature hypersurfaces · cosmological spacetimes · strong energy condition
OP-01117 Open
Harmonic-prior predictive dominance with unknown variance
ST · AIM Open Applied Problems · alpha-divergences · harmonic priors · predictive densities
OP-01118 Open
Intrinsic-flat stability of scalar sphere rigidity
DG · AIM Open Applied Problems · intrinsic flat convergence · minimal surfaces · scalar curvature
OP-01119 Open
Must observations be affine in every finite-dimensional Euclidean estimation algebra?
OC · AIM Open Applied Problems · estimation algebras · Mitter conjecture · nonlinear filtering
OP-01120 Open
Path connectedness of the full asymptotically flat vacuum constraint space
DG · AIM Open Applied Problems · asymptotically flat initial data · Einstein constraint equations
OP-01121 Open
Real-energy nullspace on nontrapping Lorentzian scattering spaces
AP · AIM Open Applied Problems · embedded eigenvalues · Feynman propagators · Klein-Gordon operators
OP-01122 Open
Residual norm attainment and differentiability of the dual norm
FA · AIM Open Applied Problems · Banach spaces · Fréchet differentiability · norm-attaining functionals
OP-01123 Open
Scalar-flat apparent-horizon extensions with prescribed Schwarzschild mass
DG · AIM Open Applied Problems · apparent horizons · Bartnik mass · scalar-flat metrics
OP-01124 Open
Scalar-flat realization of extendible Bartnik boundary data
DG · AIM Open Applied Problems · Bartnik data · scalar-flat extensions
OP-01125 Open
Sharp minimax rates for a Darcy conductivity
ST · AIM Open Applied Problems · minimax rates · statistical inverse problems
OP-01126 Open
The sharp generic bound on iterated Fuller singularities
OC · AIM Open Applied Problems · control-affine systems · Fuller singularities
OP-01127 Open
Uniform finite-ensemble accuracy under detectability
PR · AIM Open Applied Problems · detectability · ensemble Kalman filters · uniform-in-time estimates
OP-01128 Open
Uniqueness of free-time controlled transport in Eulerian form
OC · AIM Open Applied Problems · free end times · optimal control · optimal transport
OP-01129 Open
Uniqueness of the simply connected static three-dimensional hemisphere
DG · AIM Open Applied Problems · hemispheres · scalar curvature · static manifolds
OP-01130 Open
Volume-preserving intrinsic-flat compactness with minimal boundary
DG · AIM Open Applied Problems · integral currents · intrinsic flat convergence · scalar curvature
OP-01131 Open
Zero vacuum Bartnik mass without a no-horizon condition
DG · AIM Open Applied Problems · Bartnik mass · positive mass theorems · scalar-flat extensions