clopen.solutions

Open problems

980 registered problems.

OP-00270 Partially resolved
Pólya's eigenvalue inequalities
SP · AIM Open Applied Problems · Dirichlet eigenvalues · Neumann eigenvalues · Weyl's law
OP-00272 Open
The spectral honeycomb conjecture
SP · AIM Open Applied Problems · Dirichlet eigenvalues · honeycomb conjecture · spectral minimal partitions
OP-00285 Open
Dirichlet spectral determination of smooth strictly convex planar domains
SP · AIM Open Applied Problems · Dirichlet eigenvalues · inverse spectral problems · isospectral domains
OP-00296 Open
Pólya–Szegő polygonal Faber–Krahn conjecture
SP · AIM Open Applied Problems · Dirichlet eigenvalues · Faber–Krahn inequality · polygons
OP-00297 Open
The polygonal Payne–Pólya–Weinberger ratio conjecture
SP · AIM Open Applied Problems · Dirichlet eigenvalues · eigenvalue ratios · polygons
OP-00309 Open
Does the disk minimize the third Dirichlet eigenvalue?
SP · AIM Open Applied Problems · Dirichlet eigenvalues · spectral shape optimization
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-00366 Open
Is the optimal magnetic rectangle always a square?
SP · AIM Open Applied Problems · Dirichlet eigenvalues · magnetic Laplacians
OP-00759 Solution claimed
The Mercedes-star partition of a disk
SP · AIM Open Applied Problems · Dirichlet eigenvalues · spectral minimal partitions