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ON DOYLE-GRIGOR'YAN CRITERION FOR NON-PARABOLICITY

G. Pacelli Bessa,Vicent Gimeno Garcia,Leandro F. Pessoa, Alberto G. Setti

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY（2024）

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Abstract
In this short note we show that Doyle-Grigor'yan criterion for nonparabolicity is not necessary in dimension greater than or equal to four. This gives an negative answer to Problem # 1 of Grigor'yan [Bull. Amer. Math. Soc. (N.S.) 36 (1999). pp. 135-249] in this dimensional range.
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