Subharmonic functions, conformal metrics, and CAT(0)

نویسندگان

چکیده

We present an analytical proof that certain natural metric universal covers are Hadamard spaces. If $$\rho \,\mathrm{{d}}s$$ induces a complete distance d on plane domain $$\Omega $$ , and =\varphi \circ u$$ where u is (locally Lipschitz and) subharmonic in $$\varphi positive increasing interval containing $$u(\Omega )$$ with $$\log \varphi convex, then $$(\Omega ,d)$$ has cover $$({\tilde{\Omega }},{\tilde{d}})$$ which space (with geodesics have continuous first derivatives).

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ژورنال

عنوان ژورنال: Complex analysis and its synergies

سال: 2022

ISSN: ['2197-120X', '2524-7581']

DOI: https://doi.org/10.1007/s40627-021-00089-6