Radial balanced metrics on the unit disk
نویسندگان
چکیده
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 geucl-balanced of height 3 (where geucl is the standard Euclidean metric on C = R), and the function h(x) = e−Φ(z), x = |z|, 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.
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