Address: Institute of Mathematics and Statistics, Universidade Federal Fluminense, Niteroi, Brazil
E-mail:
mirjana.mmilijevic@gmail.com
luis.yapu@gmail.com
Abstract: We define cut-off functions in order to allow higher growth for Dirichlet energy. Our results are generalizations of the classical Cheng-Yau’s growth conditions of parabolicity. Finally we give some applications to the function theory of Kähler and quaternionic-Kähler manifolds.
AMSclassification: primary 53C21; secondary 53C20.
Keywords: volume growth, parabolic manifolds, weighted parabolic manifolds.
DOI: 10.5817/AM2020-1-1