Thus, if V is not Riemannian on M , we can ﬁnd an open subset U of M on which V is not Riemannian and H is integrable.
Harmonic morphisms with one-dimensional fibres on Einstein manifolds
V is Riemannian on some open subset of M ; hence, by Proposition 1.4 , V is Riemannian on (M , g ) .
Harmonic morphisms with one-dimensional fibres on Einstein manifolds
Let X be the Riemannian universal covering of a compact Riemannian manifold M = X/Γ and {H ω = ∆ + V ω }ω∈Ω be a family of Schr¨odinger operators, parameterized by elements of the probability space (Ω, A, P).
Integrated density of states for ergodic random Schr\"odinger operators on manifolds
Let X be the Riemannian universal covering of a compact Riemannian manifold M = X/Γ and assume that Γ is of polynomial growth.
Integrated density of states for ergodic random Schr\"odinger operators on manifolds
Let X be the Riemannian universal covering of a compact Riemannian manifold M = X/Γ.
Integrated density of states for ergodic random Schr\"odinger operators on manifolds
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