An Hadamard maximum principle for the biplacian on hyperbolic manifolds
Journées équations aux dérivées partielles (1999), article no. 3, 5 p.

We prove the existence of a maximum principle for operators of the type Δω-1Δ, for weights ω with logω subharmonic. It is associated with certain simply connected subdomains that are produced by a Hele-Shaw flow emanating from a given point in the domain. For constant weight, these are the circular disks in the domain. The principle is equivalent to the following statement. THEOREM. Suppose ω is logarithmically subharmonic on the unit disk, and that the weight times area measure is a reproducing measure (for the harmonic functions). Then the Green function for the Dirichlet problem associated with Δω-1Δ on the unit disk is positive.

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Hedenmalm, Håkan. An Hadamard maximum principle for the biplacian on hyperbolic manifolds. Journées équations aux dérivées partielles (1999), article  no. 3, 5 p. http://www.numdam.org/item/JEDP_1999____A3_0/

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