clopen.solutions

Open problems

980 registered problems.

OP-00527 Open
The sharp number of directions illuminating a convex body
MG · AIM Open Applied Problems · convex bodies · homothetic coverings · illumination numbers
OP-00567 Open
Matheron’s covariogram uniqueness problem in three dimensions
MG · AIM Open Applied Problems · convex bodies · covariograms · phase retrieval
OP-00653 Open
The ball as the least densely packable convex solid
MG · AIM Open Applied Problems · convex bodies · Kepler conjecture · packing densities
OP-00695 Solution claimed
The symmetric Mahler inequality in four dimensions
MG · AIM Open Applied Problems · convex bodies · Mahler conjecture · volume product
OP-00716 Solution claimed
Simplices maximize the isotropic constant
MG · AIM Open Applied Problems · convex bodies · isotropic constant · slicing problem
OP-00808 Solution claimed
Asymmetry at the Macbeath point of a convex body
MG · AIM Open Applied Problems · centers of convex bodies · convex bodies