clopen.solutions

Open problems

932 registered problems.

OP-00273 Open
The regular-polygon Steklov conjecture
SP · AIM Open Applied Problems · isoperimetric inequalities · polygons · Steklov eigenvalues
OP-00275 Open
Bareket's conjecture for simply connected planar domains
SP · AIM Open Applied Problems · isoperimetric inequalities · Robin eigenvalues
OP-00281 Solution claimed
Pólya–Szegő conjecture for the first buckling load
SP · AIM Open Applied Problems · buckling eigenvalues · clamped plates · isoperimetric inequalities
OP-00303 Open
Rayleigh's clamped-plate conjecture in higher dimensions
SP · AIM Open Applied Problems · biharmonic eigenvalues · clamped plates · isoperimetric inequalities
OP-00306 Open
The Robin eigenvalue ratio at fixed volume
SP · AIM Open Applied Problems · eigenvalue ratios · isoperimetric inequalities · Robin eigenvalues
OP-00331 Open
Baur’s high-field disk conjecture for all higher eigenvalues
SP · AIM Open Applied Problems · Dirichlet eigenvalues · isoperimetric inequalities · magnetic Laplacians
OP-00360 Open
The disk maximizes the first magnetic Neumann eigenvalue
SP · AIM Open Applied Problems · isoperimetric inequalities · magnetic Laplacians · Neumann eigenvalues
OP-00385 Open
The Weinstock inequality for convex domains in a sphere
SP · AIM Open Applied Problems · convex domains · isoperimetric inequalities · Steklov eigenvalues
OP-00493 Solution claimed
Pansu's isoperimetric conjecture in the Heisenberg group
DG · AIM Open Applied Problems · Heisenberg group · isoperimetric inequalities · sub-Riemannian geometry
OP-00509 Open
A sharp surface-area bound for the convex hull of a closed curve
MG · AIM Open Applied Problems · convex hulls · isoperimetric inequalities · space curves