clopen.solutions

Open problems

1027 registered problems.

OP-01008 Open
Sharpness of the logarithmic factor in the higher-order Cheeger–Steklov inequality
SP · Cheeger inequality · Colbois–Girouard–Gordon–Sher Steklov problems · Steklov eigenvalues
OP-01009 Open
Existence of a metric maximising a higher normalised Steklov eigenvalue
SP · Colbois–Girouard–Gordon–Sher Steklov problems · eigenvalue optimisation · Riemannian surfaces · Steklov eigenvalues
OP-01010 Open
Embeddedness of first Steklov maximisers with many boundary components
DG · Colbois–Girouard–Gordon–Sher Steklov problems · eigenvalue optimisation · free boundary minimal surfaces · Steklov eigenvalues
OP-01011 Open
Steklov critical metrics versus critical metric–density pairs
SP · Colbois–Girouard–Gordon–Sher Steklov problems · critical metrics · harmonic maps · Steklov eigenvalues
OP-01012 Open
Uniform comparison of all Steklov eigenvalues with those of a discretisation
SP · Colbois–Girouard–Gordon–Sher Steklov problems · discretisation · graphs with boundary · Steklov eigenvalues
OP-01013 Open
Does the Steklov spectrum detect boundary singularities of orbifolds?
SP · Colbois–Girouard–Gordon–Sher Steklov problems · inverse spectral problems · orbifolds · Steklov eigenvalues
OP-01014 Open
Does the Steklov spectrum detect interior singularities of orbifolds?
SP · Colbois–Girouard–Gordon–Sher Steklov problems · inverse spectral problems · orbifolds · Steklov eigenvalues
OP-01015 Open
Can a mixed Steklov–Neumann problem be isospectral to a pure Steklov problem?
SP · Colbois–Girouard–Gordon–Sher Steklov problems · isospectral manifolds · orbifolds · Steklov eigenvalues
OP-01016 Open
Does the Steklov spectrum determine the Laplace spectrum of the boundary?
SP · Colbois–Girouard–Gordon–Sher Steklov problems · inverse spectral problems · isospectral manifolds · Steklov eigenvalues
OP-01017 Open
Steklov isospectral manifolds that are not Neumann isospectral
SP · Colbois–Girouard–Gordon–Sher Steklov problems · isospectral manifolds · Steklov eigenvalues
OP-01018 Open
Steklov isospectral manifolds that are not strongly Steklov isospectral
SP · Colbois–Girouard–Gordon–Sher Steklov problems · isospectral manifolds · Robin problem · Steklov eigenvalues
OP-01019 Open
Curvature properties determined by the Steklov spectrum in dimension three and higher
SP · Colbois–Girouard–Gordon–Sher Steklov problems · inverse spectral problems · spectral invariants · Steklov eigenvalues
OP-01020 Open
Steklov spectra on forms of different degrees for manifolds
SP · Colbois–Girouard–Gordon–Sher Steklov problems · differential forms · isospectral manifolds · Steklov eigenvalues
OP-01021 Open
A Pleijel theorem for Steklov eigenfunctions in dimension three and higher
SP · Colbois–Girouard–Gordon–Sher Steklov problems · nodal domains · Pleijel theorem · Steklov eigenfunctions
OP-01022 Open
Large normalised first Steklov eigenvalue with the boundary metric fixed
SP · Colbois–Girouard–Gordon–Sher Steklov problems · eigenvalue bounds · prescribed boundary · Steklov eigenvalues
OP-01023 Open
Does the first conformal Steklov eigenvalue exceed 2π off the disk?
SP · Colbois–Girouard–Gordon–Sher Steklov problems · conformal eigenvalues · Riemannian surfaces · Steklov eigenvalues
OP-01024 Open
The Kusner–McGrath conjecture on first Steklov eigenspaces of free boundary minimal hypersurfaces
DG · Colbois–Girouard–Gordon–Sher Steklov problems · Fraser–Li conjecture · free boundary minimal surfaces · Steklov eigenvalues
OP-01025 Open
Strict monotonicity of normalised conformal Steklov eigenvalues
SP · Colbois–Girouard–Gordon–Sher Steklov problems · conformal eigenvalues · Steklov eigenvalues
OP-01026 Open
Steklov asymptotics of curvilinear polygons with reflex angles
SP · Colbois–Girouard–Gordon–Sher Steklov problems · polygons · spectral asymptotics · Steklov eigenvalues
OP-01027 Open
Recovering the angles of a curvilinear polygon from its Steklov spectrum
SP · Colbois–Girouard–Gordon–Sher Steklov problems · inverse spectral problems · polygons · Steklov eigenvalues