Abstract

Let Φ be a strictly plurisubharmonic and radial function on the unit disk D ⊂ C and let g be the Kähler metric associated to the Kähler form ω = i 2 ∂ ∂ ̄ Φ . We prove that if g is g e u c l -balanced of height 3 (where g e u c l is the standard Euclidean metric on C = R 2 ), and the function h ( x ) = e − Φ ( z ) , x = | z | 2 , extends to an entire analytic function on R , then g equals the hyperbolic metric. The proof of our result is based on a interesting characterization of the function f ( x ) = 1 − x .

Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.