Uniqueness of zero solutions to the density heat equation on non-compact weighted manifolds is established in weighted L^p spaces, with model-manifold examples showing the density decay conditions are optimal.
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Rigidity for the heat equation with density on Riemannian manifolds through a conformal change
Uniqueness of zero solutions to the density heat equation on non-compact weighted manifolds is established in weighted L^p spaces, with model-manifold examples showing the density decay conditions are optimal.