3 problems

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Shchepetilov's conjecture on the absence of discrete energy levels for the hyperbolic two-body Hamiltonian
The two-body Hamiltonian describes the quantum motion of two particles interacting on the hyperbolic plane ${\bf H}^2$ . Shchepetilov's conjecture. The two-body Hamiltonian on…
Conjectureopenconstant-curvature-spaces quantum-mechanics spectral-theoryarXiv posted 2 days ago
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Generalization of the rotational rigidity result for minimal hypersurfaces
Rotational rigidity conjecture. The result proved for minimal hypersurfaces of 5-dimensional spaces of constant curvature should generalize to a similar result in other dimensions:…
Conjectureopenconstant-curvature-spaces differential-geometry minimal-hypersurfacesarXiv posted 2 days ago
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Global continuation of Lagrange's equilateral relative equilibrium to negative curvature
Let $\kappa$ denote the constant curvature of the space, and let the family of relative equilibria be obtained by continuing Lagrange's equilateral triangle with equal masses…
Conjectureopenconstant-curvature-spaces n-body-problem relative-equilibriaarXiv posted 2 days ago

Shchepetilov's conjecture on the absence of discrete energy levels for the hyperbolic two-body Hamiltonian