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In a well-known work, M. Anderson constructed a Hadamard manifold $(M^n, g)$which carries non-zero $L^2$ harmonic $p$-forms when $p \neq n/2$, thusdisproving the Dodziuk-Singer conjecture. In this paper, we use the manifold$(M^3, g)$ in order to solve another problem in geometric analysis, namely thenonuniqueness of solutions of Leray-Hopf type of the Navier-Stokes equations.

Nonuniqueness of solutions of the Navier-Stokes equations on negatively curved Riemannian manifolds