Topological Regularity for Solutions to the Generalised Hopf Equation

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dc.citation.issue6
dc.citation.volume17
dc.contributor.authorMartin G
dc.contributor.authorYao C
dc.date.accessioned2024-07-31T19:42:05Z
dc.date.available2024-07-31T19:42:05Z
dc.date.issued2023-08-02
dc.description.abstractThe generalised Hopf equation is the first order nonlinear equation defined on a planar domain Ω ⊂ C , with data Φ a holomorphic function and η≥ 1 a positive weight on Ω , hwhw¯¯η(w)=Φ. The Hopf equation is the special case η(w) = η~ (h(w)) and reflects that h is harmonic with respect to the conformal metric η~(z)|dz| , usually η is the hyperbolic metric. This article obtains conditions on the data to ensure that a solution is open and discrete. We also prove a strong uniqueness result.
dc.description.confidentialfalse
dc.edition.editionSeptember 2023
dc.identifier.citationMartin G, Yao C. (2023). Topological Regularity for Solutions to the Generalised Hopf Equation. Complex Analysis and Operator Theory. 17. 6.
dc.identifier.doi10.1007/s11785-023-01390-4
dc.identifier.eissn1661-8262
dc.identifier.elements-typejournal-article
dc.identifier.issn1661-8254
dc.identifier.number91
dc.identifier.urihttps://mro.massey.ac.nz/handle/10179/71174
dc.publisherSpringer Nature
dc.publisher.urihttps://link.springer.com/article/10.1007/s11785-023-01390-4
dc.relation.isPartOfComplex Analysis and Operator Theory
dc.rights(c) 2023 The Author/s
dc.rightsCC BY 4.0
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectHarmonic mapping
dc.subjectHopf equation
dc.subjectFinite distortion
dc.subjectPartial differential equations
dc.subjectTopological regularity
dc.titleTopological Regularity for Solutions to the Generalised Hopf Equation
dc.typeJournal article
pubs.elements-id479912
pubs.organisational-groupCollege of Health
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