For the Parabolic Anderson model on Cartan-Hadamard manifolds, the paper establishes a curvature-dependent Dalang condition, exponential moment upper bounds with a spectral-gap term, and asymptotically matching lower bounds.
Eigenvalues of the laplacian on balls with spherically symmetric metrics
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Moment estimates for the stochastic heat equation on Cartan-Hadamard manifolds
For the Parabolic Anderson model on Cartan-Hadamard manifolds, the paper establishes a curvature-dependent Dalang condition, exponential moment upper bounds with a spectral-gap term, and asymptotically matching lower bounds.