An Hadamard maximum principle for the biplacian on hyperbolic manifolds

Håkan Hedenmalm

Håkan Hedenmalm

Journées équations aux dérivées partielles (1999), article no. 3, 5 p.

Abstract

We prove the existence of a maximum principle for operators of the type $Δ ω - 1 Δ$ , for weights $ω$ with $log ω$ 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 $Δ ω^{- 1} Δ$ on the unit disk is positive.

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

References
Cited by

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