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| A Criterion of Nonparabolicity by the Ricci Curvature* |
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Citation： |
Qing DING,Xiayu DONG.A Criterion of Nonparabolicity by the Ricci Curvature*[J].Chinese Annals of Mathematics B,2022,43(5):739~748 |
| Page view： 451
Net amount： 408 |
Authors： |
Qing DING; Xiayu DONG |
Foundation： |
National Natural Science Foundation of China (Nos.12071080, 12141104). |
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| Abstract： |
A complete manifold is said to be nonparabolic if it does admit a positive Green’s function. To ?nd a sharp geometric criterion for the parabolicity/nonparbolicity is an attractive question inside the function theory on Riemannian manifolds. This paper devotes to proving a criterion for nonparabolicity of a complete manifold weakened by the Ricci curvature. For this purpose, we shall apply the new Laplacian comparison theorem established by the ?rst author to show the existence of a non-constant bounded subharmonic function. |
Keywords： |
Nonparabolicity, Subharmonic function, Ricci curvature |
Classification： |
58E20, 58J32, 53C43, 53C20, 31C12 |
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