Open problems

980 registered problems.

OP-00088 Lean verified

Number of components of a real interval eigenvalue set

NA · interval matrices · OpenProblemsInNLA · real eigenvalues

OP-00106 Lean verified

Corrected generalized geometric-mean product conjecture

FA · eigenvalues · log-majorization · matrix geometric means · OpenProblemsInNLA

OP-00124 Lean verified

Nonnegative H-eigenvalue inheritance from odd-order Hankel tensors

NA · Hankel tensors · H-eigenvalues · OpenProblemsInNLA

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-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-00280 Open

The sharp ratio of the first two buckling eigenvalues

SP · AIM Open Applied Problems · buckling eigenvalues · clamped plates · eigenvalue ratios

OP-00281 Solution claimed

Pólya–Szegő conjecture for the first buckling load

SP · AIM Open Applied Problems · buckling eigenvalues · clamped plates · isoperimetric inequalities

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-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-00309 Open

Does the disk minimize the third Dirichlet eigenvalue?

SP · AIM Open Applied Problems · Dirichlet eigenvalues · spectral shape optimization

OP-00317 Open

Excess Floquet multiplicity for complex periodic Schrödinger equations

SP · AIM Open Applied Problems · Hill operators · non-self-adjoint operators · periodic eigenvalues

OP-00318 Solution claimed

Uniqueness of the critical catenoid

DG · AIM Open Applied Problems · critical catenoid · free boundary minimal surfaces · Steklov 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-00335 Open

Irreducibility of complex Fermi varieties

SP · AIM Open Applied Problems · embedded eigenvalues · Fermi varieties · periodic Schrödinger operators

OP-00343 Solution claimed

Arbitrarily large Steklov frequency with a prescribed embedded boundary

SP · AIM Open Applied Problems · prescribed boundary · Steklov eigenvalues · submanifolds

OP-00346 Open

The first Steklov eigenvalue of a free-boundary minimal hypersurface

DG · AIM Open Applied Problems · free boundary minimal surfaces · Steklov eigenvalues

OP-00360 Open

The disk maximizes the first magnetic Neumann eigenvalue

SP · AIM Open Applied Problems · isoperimetric inequalities · magnetic Laplacians · Neumann eigenvalues

OP-00366 Open

Is the optimal magnetic rectangle always a square?

SP · AIM Open Applied Problems · Dirichlet eigenvalues · magnetic Laplacians

OP-00385 Open

The Weinstock inequality for convex domains in a sphere

SP · AIM Open Applied Problems · convex domains · isoperimetric inequalities · Steklov eigenvalues

OP-00390 Solution claimed

Unbounded first Steklov multiplicity with fixed boundary count

SP · AIM Open Applied Problems · eigenvalue multiplicities · Riemannian surfaces · Steklov eigenvalues

OP-00395 Solution claimed

An optimal Weyl remainder for interior transmission eigenvalues

SP · AIM Open Applied Problems · interior transmission eigenvalues · non-self-adjoint operators · Weyl's law

OP-00759 Solution claimed

The Mercedes-star partition of a disk

SP · AIM Open Applied Problems · Dirichlet eigenvalues · spectral minimal partitions