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

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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 -1 Δ on the unit disk is positive.

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     title = {An {Hadamard} maximum principle for the biplacian on hyperbolic manifolds},
     booktitle = {},
     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
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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.. doi: 10.5802/jedp.547

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